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[(\(or)-227.3(derivation)-228(tree\).)]TJ
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[(The)-325.5(string)-325.4(obtained)-325.8(by)-325.2(concatenating)-326.4(all)-325.7(leaf)-325.7(symbols)-325.2(of)-325.2(a)-325.4(parse)-325.3(tree)]TJ
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[(is)-325.2(called)-325.9(its)]TJ
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[(written)-250.5(as)]TJ
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(y)Tj
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[(\()-120(\))]TJ
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[(.)-333(Every)-250.3(parse)-250.1(tree)-250.5(thus)-249.9(denotes)-250.3(a)]TJ
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(CFG)Tj
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[(-derivation)-250.7(of)-250(its)-250.2(yield.)]TJ
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[(W)39.8(ith)-269.8(respect)-270(to)-269.7(a)]TJ
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0.0615 Tc
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(G)Tj
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(V)Tj
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(T)Tj
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(,)Tj
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(R)Tj
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[(we)-269.5(call)-270.1(a)-269.7(parse)-269.6(tree)]TJ
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(lexicalized)Tj
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[(\()-120(\))]TJ
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(T)Tj
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0.3916 Tc
[(.I)391.6(f)]TJ
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()Tj
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(1)Tj
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[(,...)-166.6(,)]TJ
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(k)Tj
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[(are)-291.8(arbitrary)-292.1(parse)-291.5(trees)-291.8(and)]TJ
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(A)Tj
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(V)Tj
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[(,)-301.9(w)0(e)-291.5(call)-292.1(the)-291.8(parse)-291.6(tree)]TJ
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(1)Tj
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(k)Tj
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(a)Tj
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(frag-)Tj
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[(ment)-279.5(tr)37(ee)]TJ
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(or)Tj
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[(.)-420.9(I)0(f)-279.3(every)]TJ
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(i)Tj
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[(is)-279.3(lexicalized,)]TJ
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(A)Tj
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(\()Tj
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(1)Tj
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0.1667 Tc
()Tj
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(k)Tj
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(\))Tj
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[(is)-279.3(called)-280(a)]TJ
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[(constituent)-280(tr)37(ee)]TJ
/TT2 1 Tf
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(or)Tj
-35.667 -1.2 TD
(a)Tj
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(constituent)Tj
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[(.)-370.1(For)-262.2(example,)-266.2(the)-262.7(parse)-262.4(trees)]TJ
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(S)Tj
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(\()Tj
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0.096 Tc
(SS)Tj
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(S)Tj
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(\()Tj
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(S)Tj
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(S)Tj
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(\()Tj
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(SS)Tj
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(\)\))Tj
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(and)Tj
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(S)Tj
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(\()Tj
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(S)Tj
6.9738 0 0 6.9738 392.3288 420.0884 Tm
(S)Tj
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(\()Tj
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(S)Tj
6.9738 0 0 6.9738 406.6371 420.0884 Tm
(S)Tj
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(\()Tj
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(SS)Tj
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(\)\)\))Tj
/TT2 1 Tf
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(displayed)Tj
-32.6671 -1.2 TD
[(in)-243(derivation)-243.5(\(1\))-242.7(are)-243.1(all)-243.2(fragments,)-244.7(where)]TJ
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(S)Tj
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[(is)-242.7(not,)-244.4(because)-243.3(it)-243(is)-242.8(not)-242.9(of)-242.8(the)-243(form)]TJ
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(A)Tj
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(\()Tj
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(1)Tj
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0.1667 Tc
()Tj
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()Tj
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(k)Tj
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(\))Tj
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(.)Tj
-36.25 -1.2 TD
[(No)-249.8(parse)-250.1(tree)-250.4(displayed)-250.5(in)-250.2(\(1\))-250(is)-250(a)-250.2(constituent)-250.7(because)-250.4(not)-250.1(one)-250.2(of)-250(them)-250.5(is)-250(lexicalized.)]TJ
0 -1.8 TD
[(A)-312.7(parse)-313(tree)]TJ
/F2 1 Tf
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()Tj
/TT2 1 Tf
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[(is)-312.9(said)-313.1(to)]TJ
/TT4 1 Tf
3.9948 0 TD
(start)Tj
/TT2 1 Tf
2.1569 0 TD
[(a)-313.1(parse)-313(tree)]TJ
/F2 1 Tf
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()Tj
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6.9738 0 0 6.9738 292.4942 383.3561 Tm
()Tj
/TT2 1 Tf
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[(if)17.8(f)-312.9(there)-313.5(exists)-313.1(a)]TJ
7.9701 0 0 7.9701 366.9719 379.7397 Tm
0.0616 Tc
(CFG)Tj
9.9626 0 0 9.9626 383.6992 379.7397 Tm
0 Tc
(-derivation)Tj
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()Tj
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(=)Tj
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(1)Tj
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9.9626 0 0 9.9626 468.0847 379.7397 Tm
()Tj
-35.457 -1.2 TD
0.1667 Tc
[()-152.7()]TJ
/F2 1 Tf
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0 Tc
()Tj
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6.9738 0 0 6.9738 148.9116 366.2901 Tm
(n)Tj
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(=)Tj
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()Tj
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 175.2339 367.7845 Tm
[(.)-370.3(I)0(f)-262.4(a)-262.6(fragment)]TJ
/F2 1 Tf
6.1275 0 TD
()Tj
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[(starts)-262.6(a)-262.6(parse)-262.5(tree)]TJ
/F2 1 Tf
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()Tj
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0.8154 0 TD
[(we)-262.4(call)]TJ
/F2 1 Tf
3.1348 0 TD
()Tj
/TT2 1 Tf
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(an)Tj
/TT4 1 Tf
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[(initial)-263.2(fragment)]TJ
/TT2 1 Tf
6.5357 0 TD
(of)Tj
/F2 1 Tf
1.0955 0 TD
()Tj
/TT2 1 Tf
0.553 0 TD
[(.)-370.2(For)]TJ
-34.4908 -1.2 TD
[(a)-304.3(parse)-304.3(tree)]TJ
/F2 1 Tf
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()Tj
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[(we)-304.2(de)]TJ
/TT7 1 Tf
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()Tj
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(ne)Tj
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[(\()130()10(\))]TJ
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[(to)-304.4(be)-304.3(the)-304.4(set)-304.4(of)-304.1(all)-304.6(initial)-305.1(fragments)-304.6(of)]TJ
/F2 1 Tf
15.7912 0 TD
()Tj
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0.4954 Tc
[(.I)495.4(f)]TJ
/F2 1 Tf
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[(has)-304.1(no)-304.2(initial)]TJ
-31.2248 -1.2 TD
[(fragments,)-298.5(we)-288.4(let)]TJ
/F2 1 Tf
7.2897 0 TD
0.13 Tc
[(\()130()10(\))]TJ
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[(.)-448.2(A)-288.2(parse)-288.4(tree)-288.9(may)-288.7(also)]TJ
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(occur)Tj
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[(in)-288.6(a)-288.6(parse)-288.5(tree)-288.8(according)-289(to)-288.6(the)]TJ
-23.9957 -1.2 TD
[(following)-238.2(de)]TJ
/TT7 1 Tf
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()Tj
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[(nition.)-329.5(\(1\))]TJ
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()Tj
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6.9738 0 0 6.9738 219.4152 335.5355 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 224.1674 331.919 Tm
[(occurs)-238.1(in)]TJ
/F2 1 Tf
3.8639 0 TD
()Tj
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0.2404 Tc
[(,i)240.4(f)]TJ
/F2 1 Tf
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()Tj
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()Tj
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9.9626 0 0 9.9626 291.7759 331.919 Tm
(starts)Tj
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()Tj
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[(;)-242.2(\(2\))]TJ
/F2 1 Tf
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()Tj
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()Tj
/TT2 1 Tf
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[(occurs)-238(in)]TJ
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()Tj
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(=)Tj
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(A)Tj
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(\()Tj
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6.9738 0 0 6.9738 422.419 330.4246 Tm
(1)Tj
/F1 1 Tf
9.9626 0 0 9.9626 428.0648 331.919 Tm
0.1667 Tc
()Tj
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6.9738 0 0 6.9738 446.9938 330.4246 Tm
(i)Tj
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9.9626 0 0 9.9626 451.7679 331.919 Tm
0.1667 Tc
()Tj
/F2 1 Tf
1.334 0 TD
0 Tc
()Tj
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(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 474.7596 331.919 Tm
(\))Tj
/TT2 1 Tf
-36.127 -1.2 TD
(if)Tj
/F2 1 Tf
0.861 0 TD
()Tj
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()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 133.7983 319.9638 Tm
[(occurs)-250.1(in)]TJ
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()Tj
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(i)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 181.2852 319.9638 Tm
(.)Tj
-6.6695 -1.8 TD
[(As)-333(an)-333.5(example,)-355(consider)-333.5(the)-333.7(lexicalized)-334.6(parse)-333.4(tree)]TJ
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(=)Tj
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(S)Tj
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9.9626 0 0 9.9626 352.3955 302.0311 Tm
(\()Tj
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0.37 0 TD
(a)Tj
6.9738 0 0 6.9738 362.2317 300.5367 Tm
(A)Tj
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(\()Tj
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(a)Tj
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0.548 0 TD
(\))Tj
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6.9738 0 0 6.9738 380.5221 300.5367 Tm
(B)Tj
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9.9626 0 0 9.9626 385.7206 302.0311 Tm
(\()Tj
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6.9738 0 0 6.9738 390.127 300.5367 Tm
(A)Tj
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9.9626 0 0 9.9626 395.0257 302.0311 Tm
(\()Tj
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(a)Tj
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(\))Tj
/TT4 1 Tf
6.9738 0 0 6.9738 408.4174 300.5367 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 413.616 302.0311 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(b)Tj
/F2 1 Tf
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(\)\)\))Tj
/TT2 1 Tf
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[(.)-583(The)-333.6(con-)]TJ
-32.0017 -1.2 TD
(stituents)Tj
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(A)Tj
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9.9626 0 0 9.9626 156.3288 290.076 Tm
(\()Tj
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0.37 0 TD
(a)Tj
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(\))Tj
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(,)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 174.946 288.5815 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 180.1445 290.076 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(b)Tj
/F2 1 Tf
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(\))Tj
/TT2 1 Tf
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(,)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 198.5126 288.5815 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 203.7111 290.076 Tm
(\()Tj
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6.9738 0 0 6.9738 208.1176 288.5815 Tm
(A)Tj
/F2 1 Tf
9.9626 0 0 9.9626 213.0162 290.076 Tm
(\()Tj
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0.37 0 TD
(a)Tj
/F2 1 Tf
0.548 0 TD
(\))Tj
/TT4 1 Tf
6.9738 0 0 6.9738 226.408 288.5815 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 231.6065 290.076 Tm
(\()Tj
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0.373 0 TD
(b)Tj
/F2 1 Tf
0.52 0 TD
(\)\))Tj
/TT2 1 Tf
1.0156 0 TD
(and)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 268.0479 288.5815 Tm
(S)Tj
/F2 1 Tf
9.9626 0 0 9.9626 272.3467 290.076 Tm
(\()Tj
/TT4 1 Tf
0.37 0 TD
0.147 Tc
(aA)Tj
6.9738 0 0 6.9738 289.2952 288.5815 Tm
0 Tc
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 294.4937 290.076 Tm
(\()Tj
/TT4 1 Tf
0.472 0 TD
0.0962 Tc
(AB)Tj
/F2 1 Tf
1.381 0 TD
0 Tc
(\)\))Tj
/TT2 1 Tf
1.0156 0 TD
[(all)-270.1(occur)-269.9(in)]TJ
/F2 1 Tf
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()Tj
/TT2 1 Tf
0.553 0 TD
[(.)-391.8(The)-269.9(fragment)]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 440.2311 288.5815 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 445.4296 290.076 Tm
(\()Tj
/TT4 1 Tf
0.472 0 TD
(A)Tj
6.9738 0 0 6.9738 456.9485 288.5815 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 462.147 290.076 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(b)Tj
/F2 1 Tf
0.52 0 TD
(\)\))Tj
/TT2 1 Tf
-35.754 -1.2 TD
[(occurs)-250.1(in)]TJ
/F2 1 Tf
3.888 0 TD
()Tj
/TT2 1 Tf
0.803 0 TD
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(C)Tj
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[(to)-287(denote)-287.3(the)-287.1(restriction)-287.5(of)-286.8(the)-287.1(set)-287(to)-287(constituents)-287.4(of)-286.8(category)]TJ
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(A)Tj
/TT2 1 Tf
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(.)Tj
-36.25 -1.2 TD
[(Analogous)-250(to)-250.2(the)-250.2(de)]TJ
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()Tj
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[(nition)-250.5(above,)]TJ
/F2 1 Tf
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()Tj
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([)Tj
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(C)Tj
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(A)Tj
/TT2 1 Tf
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[(])-250(then)-250.3(denotes)-250.3(the)-250.2(set)-250.2(of)-250(all)-250.5(initial)-250.9(fragments)-250.5(of)]TJ
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(A)Tj
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(.)Tj
-36.1687 -1.8 TD
[(The)-183(total)-183.3(number)-183(of)-182.6(instances)-183.2(of)-182.6(a)-182.9(parse)-182.8(tree)]TJ
/F2 1 Tf
17.4169 0 TD
()Tj
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[(in)-182.9(a)-182.8(corpus)]TJ
/F4 1 Tf
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(T)Tj
/TT2 1 Tf
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[(is)-182.7(de)]TJ
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()Tj
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[(ned)-182.8(by)]TJ
/TT4 1 Tf
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(f)Tj
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(\()Tj
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(;)Tj
/F2 1 Tf
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()Tj
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(1)Tj
/F2 1 Tf
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0.1666 Tc
[(,...)-166.8(,)]TJ
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(n)Tj
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(\))Tj
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(=)Tj
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()Tj
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(n)Tj
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(i)Tj
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(=)Tj
/TT2 1 Tf
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(1)Tj
/TT4 1 Tf
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(f)Tj
/F2 1 Tf
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(\()Tj
/F1 1 Tf
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(;)Tj
/F2 1 Tf
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()Tj
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(i)Tj
/F2 1 Tf
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(\))Tj
/TT2 1 Tf
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[(.)-398.3(I)0(n)-271.7(case)-272(it)-272(is)-271.8(clear)-272.3(which)-271.9(treebank)-272.3(is)-271.7(meant,)]TJ
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(f)Tj
/F2 1 Tf
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(\()Tj
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(;)Tj
/F2 1 Tf
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()Tj
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(1)Tj
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0.1667 Tc
[(,...)-166.6(,)0()]TJ
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(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 414.6331 603.6202 Tm
(\))Tj
/TT2 1 Tf
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[(may)-272.1(be)-271.9(abbre-)]TJ
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[(viated)-266.3(to)]TJ
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(f)Tj
/F2 1 Tf
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[(\()-120(\))]TJ
/TT2 1 Tf
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[(.)-380.2(Given)-265.9(a)-265.9(parse)-265.8(tree)]TJ
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()Tj
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()Tj
T*
()Tj
/TT4 1 Tf
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(T)Tj
/TT2 1 Tf
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[(,)-269.7(the)]TJ
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[(r)37.2(elative)-266.7(occurr)37(ence)-266.2(fr)37.1(equency)]TJ
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(or)Tj
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[(r)37.2(elative)-266.6(fr)37(e-)]TJ
-31.8094 -1.2 TD
[(quency)-320.5(F)]TJ
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[(\()-120(\))]TJ
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(of)Tj
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()Tj
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(in)Tj
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(T)Tj
/TT2 1 Tf
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[(is)-250(de)]TJ
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()Tj
/TT2 1 Tf
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[(ned)-250.1(as)]TJ
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(F)Tj
/F2 1 Tf
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[(\()-120(\))]TJ
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(=)Tj
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(f)Tj
/F2 1 Tf
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[(\()-120(\)/)]TJ
/TT4 1 Tf
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(f)Tj
/F2 1 Tf
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(\()Tj
/TT4 1 Tf
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(r)Tj
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[(\()-120(\)\))]TJ
/TT2 1 Tf
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(.)Tj
/TT6 1 Tf
11.9552 0 0 11.9552 114.8394 545.2789 Tm
[(1.2)-1000(The)-250(Classical)]TJ
9.5641 0 0 9.5641 213.1099 545.279 Tm
0.0619 Tc
(DOP)Tj
11.9552 0 0 11.9552 237.7614 545.2791 Tm
0 Tc
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/TT2 1 Tf
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[(T)69.8(o)-216(generate)-216.8(a)-216.3(new)-216(sentence)-216.6(from)-216.2(fragments)-216.5(present)-216.3(in)-216.2(the)-216.4(corpus,)-222.8(the)]TJ
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0.0616 Tc
(DOP)Tj
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0 Tc
[(model)-216.5(de)]TJ
/TT7 1 Tf
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()Tj
/TT2 1 Tf
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[(nes)-216(the)]TJ
-33.729 -1.2 TD
[(composition)-238.5(operation)-238.3(of)]TJ
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[(leftmost)-238.2(substitution)]TJ
/TT2 1 Tf
8.0727 0 TD
[(,)-240.2(a)-238(partial)-238.6(function)-238.3(on)-237.8(pairs)-238(of)-237.8(fragments.)-329.4(The)]TJ
-18.3411 -1.2 TD
[(composition)-215.8(of)-215.1(fragments)]TJ
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()Tj
/TT2 1 Tf
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(and)Tj
/F2 1 Tf
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()Tj
/TT2 1 Tf
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[(,)-222.1(written)-215.6(as)]TJ
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()Tj
/F1 1 Tf
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( )Tj
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()Tj
/TT2 1 Tf
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[(is)-215.1(de)]TJ
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()Tj
/TT2 1 Tf
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[(ned)-215.2(if)-215.3(\(and)-215.3(only)-215.3(if\))-215.2(the)-215.4(label)-215.7(of)]TJ
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()Tj
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(is)Tj
-35.833 -1.2 TD
[(identical)-219.3(to)-218.5(the)-218.6(leftmost)-218.9(nonterminal)-219.2(of)]TJ
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()Tj
/TT2 1 Tf
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[(.I)322.5(f)]TJ
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()Tj
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( )Tj
/F2 1 Tf
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()Tj
/TT2 1 Tf
0.8523 0 TD
[(is)-218.2(de)]TJ
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()Tj
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[(ned,)-224.9(it)-218.5(denotes)-218.6(a)-218.5(copy)-218.5(of)]TJ
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()Tj
/TT2 1 Tf
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[(in)-218.5(which)]TJ
-33.0597 -1.2 TD
[(a)-250.2(copy)-250.2(of)]TJ
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()Tj
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[(has)-250(been)-250.3(substituted)-250.4(for)-250(the)-250.3(leftmost)-250.6(nonterminal)-250.9(of)]TJ
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()Tj
/TT2 1 Tf
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[(.)-333(For)-249.8(example)]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 221.8909 449.4184 Tm
(A)Tj
/F2 1 Tf
9.9626 0 0 9.9626 226.7896 450.9128 Tm
(\()Tj
/TT4 1 Tf
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(B)Tj
6.9738 0 0 6.9738 237.9497 449.4184 Tm
(C)Tj
/F2 1 Tf
9.9626 0 0 9.9626 243.7061 450.9128 Tm
(\()Tj
/TT4 1 Tf
0.449 0 TD
0.1392 Tc
(BD)Tj
/F2 1 Tf
1.514 0 TD
0 Tc
(\)\))Tj
/F1 1 Tf
0.9682 0 TD
( )Tj
/TT4 1 Tf
6.9738 0 0 6.9738 280.6336 449.4184 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 285.8322 450.9128 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(b)Tj
/F2 1 Tf
0.52 0 TD
(\))Tj
/F1 1 Tf
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(=)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 312.4414 449.4184 Tm
(A)Tj
/F2 1 Tf
9.9626 0 0 9.9626 317.34 450.9128 Tm
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 321.5861 449.4184 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 326.7846 450.9128 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(b)Tj
/F2 1 Tf
0.52 0 TD
(\))Tj
/TT4 1 Tf
6.9738 0 0 6.9738 339.3694 449.4184 Tm
(C)Tj
/F2 1 Tf
9.9626 0 0 9.9626 345.1258 450.9128 Tm
(\()Tj
/TT4 1 Tf
0.449 0 TD
0.1392 Tc
(BD)Tj
/F2 1 Tf
1.514 0 TD
0 Tc
(\)\))Tj
/TT2 1 Tf
-25.078 -2.2 TD
[(while)-207.2(the)-207.3(composition)]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 205.2912 427.5006 Tm
(A)Tj
/F2 1 Tf
9.9626 0 0 9.9626 210.1898 428.995 Tm
(\()Tj
/TT4 1 Tf
0.449 0 TD
(B)Tj
6.9738 0 0 6.9738 221.3499 427.5006 Tm
(C)Tj
/F2 1 Tf
9.9626 0 0 9.9626 227.1064 428.995 Tm
(\()Tj
/TT4 1 Tf
0.449 0 TD
0.1392 Tc
(BD)Tj
/F2 1 Tf
1.514 0 TD
0 Tc
(\)\))Tj
/F1 1 Tf
0.853 0 TD
( )Tj
/TT4 1 Tf
6.9738 0 0 6.9738 261.7385 427.5006 Tm
(D)Tj
/F2 1 Tf
9.9626 0 0 9.9626 267.5646 428.995 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(d)Tj
/F2 1 Tf
0.575 0 TD
(\))Tj
/TT2 1 Tf
0.5799 0 TD
[(is)-207(unde)]TJ
/TT7 1 Tf
2.8178 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(ned.)-318.7(The)-207.3(requirement)-207.8(to)-207.2(substitute)-207.3(on)-207(the)]TJ
/TT4 1 Tf
-20.2317 -1.2 TD
(leftmost)Tj
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3.4269 0 TD
[(nonterminal)-251(makes)-250.2(the)-250.3(composition)-250.7(operation)-250.5(unique.)]TJ
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(A)Tj
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[(leftmost)-312.5(derivation)]TJ
/F2 1 Tf
7.902 0 TD
()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 209.5542 397.6127 Tm
(1)Tj
/F1 1 Tf
9.9626 0 0 9.9626 216.5808 399.1071 Tm
0.1667 Tc
[( )-138.6()-138.6( )]TJ
/F2 1 Tf
3.0833 0 TD
0 Tc
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 252.9873 397.6127 Tm
(n)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 260.3945 399.1071 Tm
[(of)-312.1(a)-312.3(constituent)]TJ
/F2 1 Tf
6.6022 0 TD
()Tj
/TT2 1 Tf
0.865 0 TD
[(starts)-312.3(with)-312.2(an)-312.3(initial)-313(fragment)]TJ
/F2 1 Tf
12.3372 0 TD
()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 463.3873 397.6127 Tm
(1)Tj
/F1 1 Tf
9.9626 0 0 9.9626 472.2092 399.1071 Tm
()Tj
/F2 1 Tf
-35.871 -1.2 TD
0.13 Tc
[(\()130()10(\))]TJ
/TT2 1 Tf
1.963 0 TD
0 Tc
[(.)-315.6(Then,)]TJ
/F2 1 Tf
3.0788 0 TD
()Tj
/TT2 1 Tf
0.7507 0 TD
[(is)-197.7(constructed)-198.3(by)-197.7(repeatedly)-198.6(substituting)-198.1(a)-198(fragment)]TJ
/F2 1 Tf
20.5479 0 TD
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 382.948 385.6575 Tm
(k)Tj
/F1 1 Tf
0.504 0 TD
(+)Tj
/TT2 1 Tf
0.78 0 TD
(1)Tj
9.9626 0 0 9.9626 397.8571 387.1519 Tm
[(for)-197.7(the)-198(leftmost)-198.4(non-)]TJ
-28.4079 -1.2 TD
[(terminal)-250.9(of)-250(the)-250.3(fragment)]TJ
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9.9979 0 TD
(\(\(\()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 231.2817 373.7024 Tm
(1)Tj
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( )Tj
/F2 1 Tf
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()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 250.3642 373.7024 Tm
(2)Tj
/F2 1 Tf
9.9626 0 0 9.9626 254.3492 375.1967 Tm
(\))Tj
/F1 1 Tf
0.5397 0 TD
0.1667 Tc
()Tj
/F2 1 Tf
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0 Tc
(\))Tj
/F1 1 Tf
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( )Tj
/F2 1 Tf
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()Tj
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6.9738 0 0 6.9738 291.8297 373.7024 Tm
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 295.8426 375.1967 Tm
(\))Tj
/TT2 1 Tf
0.373 0 TD
[(.)-333(For)-249.8(example)]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 182.9629 351.7845 Tm
(A)Tj
/F2 1 Tf
9.9626 0 0 9.9626 187.8615 353.279 Tm
(\()Tj
/TT4 1 Tf
0.449 0 TD
0.0592 Tc
(BC)Tj
/F2 1 Tf
1.424 0 TD
0 Tc
(\))Tj
/F1 1 Tf
0.5952 0 TD
( )Tj
/TT4 1 Tf
6.9738 0 0 6.9738 220.1764 351.7845 Tm
(B)Tj
/F2 1 Tf
9.9626 0 0 9.9626 225.3748 353.279 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(b)Tj
/F2 1 Tf
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(\))Tj
/F1 1 Tf
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( )Tj
/TT4 1 Tf
6.9738 0 0 6.9738 247.3694 351.7845 Tm
(C)Tj
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9.9626 0 0 9.9626 253.1258 353.279 Tm
(\()Tj
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(D)Tj
6.9738 0 0 6.9738 265.6917 351.7845 Tm
(E)Tj
/F2 1 Tf
9.9626 0 0 9.9626 271.0785 353.279 Tm
(\()Tj
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(e)Tj
/F2 1 Tf
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(\)\))Tj
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( )Tj
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6.9738 0 0 6.9738 296.7881 351.7845 Tm
(D)Tj
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9.9626 0 0 9.9626 302.6142 353.279 Tm
(\()Tj
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(d)Tj
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(\))Tj
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(=)Tj
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6.9738 0 0 6.9738 329.7704 351.7845 Tm
(A)Tj
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9.9626 0 0 9.9626 334.669 353.279 Tm
(\()Tj
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6.9738 0 0 6.9738 338.9151 351.7845 Tm
(B)Tj
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9.9626 0 0 9.9626 344.1136 353.279 Tm
(\()Tj
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(b)Tj
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(\))Tj
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6.9738 0 0 6.9738 356.6984 351.7845 Tm
(C)Tj
/F2 1 Tf
9.9626 0 0 9.9626 362.4548 353.279 Tm
(\()Tj
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6.9738 0 0 6.9738 366.7009 351.7845 Tm
(D)Tj
/F2 1 Tf
9.9626 0 0 9.9626 372.527 353.279 Tm
(\()Tj
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0.373 0 TD
(d)Tj
/F2 1 Tf
0.575 0 TD
(\))Tj
/TT4 1 Tf
6.9738 0 0 6.9738 386.1689 351.7845 Tm
(E)Tj
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9.9626 0 0 9.9626 391.5557 353.279 Tm
(\()Tj
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(e)Tj
/F2 1 Tf
0.464 0 TD
(\)\)\))Tj
/TT2 1 Tf
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[(Bod)-198.3(de)]TJ
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2.8091 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(nes)-198.2(the)-198.6(probability)-199(of)-198.3(substituting)-198.7(a)-198.4(fragment)]TJ
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17.8867 0 TD
()Tj
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(=)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 346.6481 329.8667 Tm
(A)Tj
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(\()Tj
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6.9738 0 0 6.9738 360.9514 329.8667 Tm
(1)Tj
/F1 1 Tf
9.9626 0 0 9.9626 366.5973 331.3611 Tm
0.1667 Tc
()Tj
/F2 1 Tf
1.334 0 TD
0 Tc
()Tj
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6.9738 0 0 6.9738 385.5761 329.8667 Tm
(k)Tj
/F2 1 Tf
9.9626 0 0 9.9626 389.5891 331.3611 Tm
(\))Tj
/TT2 1 Tf
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[(for)-198.3(a)-198.4(non-terminal)]TJ
/TT4 1 Tf
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(A)Tj
/TT2 1 Tf
0.631 0 TD
(,)Tj
-36.25 -1.2 TD
[(as)-185.6(the)-185.8(number)-185.9(of)-185.6(occurrences)-186.1(of)]TJ
/F2 1 Tf
12.6644 0 TD
()Tj
/TT2 1 Tf
0.7966 0 TD
[(in)-185.8(the)-185.9(treebank,)-199(divided)-186.1(by)-185.6(the)-185.8(total)-186.3(number)-185.9(of)-185.6(occurrences)]TJ
-13.461 -1.2 TD
[(of)-250(fragments)-250.4(with)-250.2(label)]TJ
/TT4 1 Tf
9.6529 0 TD
(A)Tj
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0.861 0 TD
[(to)-250.2(be)-250.2(given)-250.3(by)-250(the)-250.3(probability)-250.7(function)]TJ
/TT4 1 Tf
15.7529 0 TD
(p)Tj
/F1 1 Tf
6.9738 0 0 6.9738 341.8062 696.9004 Tm
()Tj
/TT2 1 Tf
9.9626 0 0 9.9626 345.2942 693.2839 Tm
(:)Tj
/F2 1 Tf
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()Tj
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([)Tj
/F4 1 Tf
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(C)Tj
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(])Tj
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()Tj
/TT2 1 Tf
1.3768 0 TD
([0)Tj
/F2 1 Tf
0.833 0 TD
(,)Tj
/TT2 1 Tf
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[(1],)-250(with)]TJ
/TT4 1 Tf
-14.3968 -2.0198 TD
(p)Tj
/F1 1 Tf
6.9738 0 0 6.9738 261.5084 677.2759 Tm
()Tj
/F2 1 Tf
9.9626 0 0 9.9626 263.8894 673.1614 Tm
[(\()-40(\))]TJ
/F1 1 Tf
1.6348 0 TD
(=)Tj
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/F1 1 Tf
6.9738 0 0 6.9738 295.6962 677.2759 Tm
()Tj
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/F2 1 Tf
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[(\()-40(\))]TJ
/TT4 1 Tf
9.9626 0 0 9.9626 317.7295 673.1614 Tm
(F)Tj
/F2 1 Tf
0.702 0 TD
[(\()-40(\))]TJ
/TT2 1 Tf
14.2669 0 TD
(\(8\))Tj
-35.334 -2.5477 TD
[(Fragment)-279.4(probability)-279.7(as)-279(de)]TJ
/TT7 1 Tf
10.8356 0 TD
()Tj
/TT2 1 Tf
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[(ned)-279.1(in)-279.1(\(8\))-279(may)-279.2(be)-279.2(used)-278.9(by)-279(an)]TJ
7.9701 0 0 7.9701 348.7552 647.7795 Tm
0.0614 Tc
(STSG)Tj
9.9626 0 0 9.9626 372.7343 647.7795 Tm
0 Tc
[(as)-279(the)-279.2(probability)-279.7(function)]TJ
-25.8862 -1.2 TD
[(on)-214.9(elementary)-216(trees.)-321.6(This)-215.1(is)-214.9(permitted)-215.9(only)-215.2(if)-215.1(the)-215.2(sum)-214.9(of)]TJ
/TT4 1 Tf
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(p)Tj
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()Tj
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9.9626 0 0 9.9626 349.3639 635.8244 Tm
[(over)-215.1(all)-215.4(fragments)-215.4(of)-214.9(a)-215(particular)]TJ
-23.5404 -1.2 TD
[(category)-240.8(is)-240.3(equal)-240.7(to)-240.4(unity)64.7(.)-329.8(W)79.8(e)-240.4(will)-240.6(consider)-240.5(this)-240.4(in)-240.4(theorem)-240.9(2.1)-240.2(on)-240.3(page)-240.5(8.)]TJ
7.9701 0 0 7.9701 411.1542 623.8692 Tm
0.0616 Tc
(DOP)Tj
9.9626 0 0 9.9626 430.7129 623.8692 Tm
0 Tc
[(parsers)-240.2(may)]TJ
-31.7058 -1.2 TD
[(employ)-332.2(this)-331.8(distribution,)-352.8(keeping)]TJ
7.9701 0 0 7.9701 252.7731 611.9141 Tm
0.0616 Tc
(DOP)Tj
9.9626 0 0 9.9626 269.9377 611.9142 Tm
0 Tc
[(s)-331.5(original)-332.3(combination)-332.6(process)-331.7(of)-331.7(constructing)-332.2(new)]TJ
-15.568 -1.2 TD
[(parse)-287(trees)-287.3(from)-287.1(corpus)-287(fragments)-287.4(intact.)-444.6(A)-286.7(parse)-287.1(tree)-287.4(probability)-287.7(is)-287(then)-287.2(de)]TJ
/TT7 1 Tf
30.7319 0 TD
()Tj
/TT2 1 Tf
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[(ned)-287.1(as)-286.9(usual.)]TJ
-31.2881 -1.2 TD
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/F2 1 Tf
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()Tj
/TT2 1 Tf
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[(be)-261.3(a)-261.3(parse)-261.2(tree)-261.6(with)]TJ
/TT4 1 Tf
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(n)Tj
/TT2 1 Tf
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[(possible)-261.2(derivations)]TJ
/TT4 1 Tf
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(d)Tj
/TT2 1 Tf
6.9738 0 0 6.9738 314.4797 586.5093 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 318.4648 588.0037 Tm
0.1667 Tc
[(,...)-166.6(,)]TJ
/TT4 1 Tf
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0 Tc
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6.9738 0 0 6.9738 348.2232 586.5093 Tm
(n)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 352.5221 588.0037 Tm
[(.)-366.3(Each)-261.6(derivation)]TJ
/TT4 1 Tf
7.1924 0 TD
(d)Tj
6.9738 0 0 6.9738 430.3024 586.5093 Tm
(j)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 436.0239 588.0037 Tm
[(consists)-261.1(of)]TJ
/TT4 1 Tf
-32.2389 -1.2 TD
(m)Tj
6.9738 0 0 6.9738 123.7639 574.5541 Tm
(j)Tj
/TT2 1 Tf
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(fragments)Tj
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()Tj
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(1)Tj
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9.9626 0 0 9.9626 186.14 576.0485 Tm
( )Tj
/F2 1 Tf
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()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 198.3253 574.5541 Tm
(2)Tj
/TT4 1 Tf
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(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 207.5916 576.0485 Tm
0.1522 Tc
[( )-14.5()-14.4()0( )]TJ
/F2 1 Tf
2.6238 0 TD
0 Tc
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 239.4202 574.5541 Tm
(m)Tj
4.9813 0 0 4.9813 245.6837 573.5081 Tm
(j)Tj
6.9738 0 0 6.9738 249.1985 574.5541 Tm
(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 255.0864 576.0485 Tm
(=)Tj
/F2 1 Tf
1.0578 0 TD
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(.)Tj
/TT2 1 Tf
0.9968 0 TD
0 Tc
[(The)-224.1(probability)]TJ
/TT4 1 Tf
6.4796 0 TD
(P)Tj
/F2 1 Tf
0.693 0 TD
[(\()-120(\))]TJ
/TT2 1 Tf
1.5228 0 TD
[(of)-223.8(the)-224.1(parse)-223.9(tree)]TJ
/F2 1 Tf
6.5592 0 TD
()Tj
/TT2 1 Tf
0.7769 0 TD
[(is)-223.8(given)-224.1(by)]TJ
/TT4 1 Tf
-20.0654 -2.9783 TD
(P)Tj
/F2 1 Tf
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[(\()-120(\))]TJ
/F1 1 Tf
1.5767 0 TD
(=)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 273.6667 557.9445 Tm
(n)Tj
/F5 1 Tf
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()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 270.3642 535.387 Tm
(j)Tj
/F1 1 Tf
0.376 0 TD
(=)Tj
/TT2 1 Tf
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(1)Tj
/TT4 1 Tf
1.1261 3.394 TD
(m)Tj
4.9813 0 0 4.9813 292.543 558.0102 Tm
(j)Tj
/F5 1 Tf
9.9626 0 0 9.9626 284.276 555.8413 Tm
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 284.802 535.387 Tm
(i)Tj
/F1 1 Tf
0.375 0 TD
(=)Tj
/TT2 1 Tf
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(1)Tj
9.9626 0 0 9.9626 298.5783 546.3768 Tm
(2)Tj
/F1 1 Tf
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()Tj
/TT4 1 Tf
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(N)Tj
/F2 1 Tf
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(\()Tj
/TT4 1 Tf
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0.1612 Tc
(ij)Tj
/F2 1 Tf
6.9738 0 0 6.9738 326.0404 550.4914 Tm
0 Tc
(\))Tj
/TT4 1 Tf
9.9626 0 0 9.9626 329.8371 546.3768 Tm
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 346.1868 544.8824 Tm
0.1612 Tc
(ij)Tj
/F2 1 Tf
9.9626 0 0 9.9626 352.3687 546.3768 Tm
0 Tc
(\).)Tj
/TT2 1 Tf
11.492 0 TD
(\(9\))Tj
/TT6 1 Tf
-35.334 -4.0992 TD
[(2.1.1)-1000(Pr)17.7(operties)-250.3(of)-249.9(the)-250(Fragment)-250.3(Distribution)]TJ
/TT2 1 Tf
0 -2.3999 TD
[(In)-208.5(this)-208.7(section)-209(we)-208.5(will)-208.8(consider)-208.8(the)-208.8(question)-208.7(wether)-208.8(the)-208.8(fragment)-209.1(distribution)]TJ
/F2 1 Tf
30.4989 0 TD
0.09 Tc
[(\()90()50(\))]TJ
/F1 1 Tf
2.3017 0 TD
0 Tc
(=)Tj
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(2)Tj
/F1 1 Tf
6.9738 0 0 6.9738 457.1398 485.245 Tm
()Tj
/TT4 1 Tf
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(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-40(\))]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 114.8394 469.6734 Tm
[(is)-250(really)-250.5(a)-250.2(distribution.)-333.7(More)-249.9(speci)]TJ
/TT7 1 Tf
13.8035 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(cally)64.2(,)-250(w)0(e)-250(investigate)-250.9(whether)]TJ
/F5 1 Tf
1.1698 -1.0698 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 265.4337 438.5053 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
0.1299 Tc
[(\()129.9()9.9(\))]TJ
9.9626 0 0 9.9626 289.4307 449.5509 Tm
0.09 Tc
[(\()90()50(\))]TJ
/F1 1 Tf
2.3018 0 TD
0 Tc
(=)Tj
/TT2 1 Tf
1.0577 0 TD
(1)Tj
-20.8841 -2.9404 TD
[(holds)-250(for)-250(all)-250.4(conceivable)-251.1(constituents)]TJ
/F2 1 Tf
15.1368 0 TD
()Tj
/TT2 1 Tf
0.553 0 TD
(.)Tj
-15.6898 -1.728 TD
[(Given)-304.1(a)-304.2(fragment)]TJ
/F2 1 Tf
7.4098 0 TD
()Tj
/F1 1 Tf
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()Tj
/F2 1 Tf
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0.13 Tc
[(\()130()10(\))]TJ
/TT2 1 Tf
2.267 0 TD
0 Tc
[(we)-303.9(de)]TJ
/TT7 1 Tf
2.4137 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(ne)-304.1(the)-304.2(restricted)-304.7(subset)]TJ
/F2 1 Tf
9.6027 0 TD
()Tj
6.9738 0 0 6.9738 362.2715 401.5469 Tm
()Tj
9.9626 0 0 9.9626 367.0306 403.0413 Tm
[(\()-120(\))]TJ
/F1 1 Tf
1.7573 0 TD
(\012)Tj
/F2 1 Tf
1.2383 0 TD
0.054 Tc
[(\()54()-66(\))]TJ
/TT2 1 Tf
2.087 0 TD
0 Tc
[(to)-304.1(be)-304.1(the)-304.2(set)-304.1(of)]TJ
-30.3963 -1.2 TD
[(derivations)-250.5(of)]TJ
/F2 1 Tf
5.7769 0 TD
()Tj
/TT2 1 Tf
0.803 0 TD
[(that)-250.5(are)-250.3(started)-250.4(by)]TJ
/F2 1 Tf
7.3869 0 TD
()Tj
/TT2 1 Tf
0.611 0 TD
[(,)-250(i.e.)]TJ
/F2 1 Tf
-7.4346 -2.0198 TD
()Tj
6.9738 0 0 6.9738 190.2884 369.4692 Tm
()Tj
9.9626 0 0 9.9626 195.0476 370.9636 Tm
[(\()-120(\))]TJ
/F1 1 Tf
1.5768 0 TD
0.2778 Tc
(={)Tj
/TT4 1 Tf
1.4278 0 TD
0 Tc
(d)Tj
6.9738 0 0 6.9738 231.1064 369.4692 Tm
(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 236.9933 370.9636 Tm
()Tj
/F2 1 Tf
0.9068 0 TD
0.054 Tc
[(\()54()-66(\))]TJ
/TT2 1 Tf
2.0608 0 TD
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/F2 1 Tf
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()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 277.7833 369.4692 Tm
(1)Tj
/TT4 1 Tf
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(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 287.748 370.9636 Tm
0.2223 Tc
[( )55.7()55.6()0.1( )]TJ
/F2 1 Tf
2.834 0 TD
0 Tc
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 321.6707 369.4692 Tm
(d)Tj
4.9813 0 0 4.9813 325.9746 368.4232 Tm
(j)Tj
6.9738 0 0 6.9738 329.4894 369.4692 Tm
(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 335.3773 370.9636 Tm
(=)Tj
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()Tj
/TT2 1 Tf
0.8029 0 TD
(and)Tj
/F2 1 Tf
1.694 0 TD
()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 376.4802 369.4692 Tm
(1)Tj
/TT4 1 Tf
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(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 386.9988 370.9636 Tm
(=)Tj
/F2 1 Tf
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()Tj
/F1 1 Tf
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(})Tj
/TT2 1 Tf
-28.9868 -2.0198 TD
[(Thus,)-262.3(a)-260.1(fragment)]TJ
/F2 1 Tf
7.0861 0 TD
()Tj
/TT2 1 Tf
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[(partitions)-260.5(the)-260.2(set)-260(of)-259.9(derivations)-260.4(of)]TJ
/F2 1 Tf
13.7801 0 TD
()Tj
/TT2 1 Tf
0.8129 0 TD
[(in)-260.1(subsets)]TJ
/F2 1 Tf
4.1867 0 TD
()Tj
6.9738 0 0 6.9738 385.4914 349.3467 Tm
()Tj
9.9626 0 0 9.9626 390.2506 350.8411 Tm
[(\()-120(\))]TJ
/TT2 1 Tf
1.5589 0 TD
[(of)-259.9(derivations)-260.4(that)]TJ
-29.2033 -1.2 TD
[(start)-221.4(with)]TJ
/F2 1 Tf
3.9423 0 TD
()Tj
/TT2 1 Tf
0.611 0 TD
[(.)-323.3(W)79.8(e)-221.4(may)-221.4(prove)-221.3(the)-221.4(lemma)-221.9(below)64.8(,)-227(simply)-221.4(by)-221.1(using)-221.2(the)-221.4(distribution)-221.8(of)-221.2(cardinality)]TJ
-4.5533 -1.2 TD
[(over)-250.1(the)-250.3(disjoint)-250.4(subsets)-249.8(of)-250(this)-250.1(partition,)-250.8(given)-250.3(by)]TJ
/F1 1 Tf
10.5105 -2.8858 TD
(|)Tj
/F2 1 Tf
0.286 0 TD
0.054 Tc
[(\()54()-66(\))]TJ
/F1 1 Tf
1.783 0 TD
0.2778 Tc
(|=)Tj
/F5 1 Tf
1.6215 1.75 TD
0 Tc
()Tj
0 -0.6 TD
()Tj
T*
()Tj
T*
()Tj
T*
()Tj
0.8326 1.6 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 259.5567 287.1349 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
0.13 Tc
[(\()130()10(\))]TJ
9.9626 0 0 9.9626 283.5547 298.1805 Tm
0 Tc
()Tj
6.9738 0 0 6.9738 287.8386 296.6862 Tm
()Tj
9.9626 0 0 9.9626 292.5978 298.1805 Tm
[(\()-120(\))]TJ
/F5 1 Tf
1.299 1.75 TD
()Tj
0 -0.6 TD
()Tj
T*
()Tj
T*
()Tj
T*
()Tj
/F1 1 Tf
0.6028 0.65 TD
(=)Tj
/F5 1 Tf
1.4713 0.95 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 322.0822 287.1349 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
0.13 Tc
[(\()130()10(\))]TJ
/F1 1 Tf
9.9626 0 0 9.9626 346.0802 298.1805 Tm
0 Tc
(|)Tj
/F2 1 Tf
0.286 0 TD
()Tj
6.9738 0 0 6.9738 353.2135 296.6862 Tm
()Tj
9.9626 0 0 9.9626 357.9727 298.1805 Tm
[(\()-120(\))]TJ
/F1 1 Tf
1.299 0 TD
(|)Tj
/TT6 1 Tf
-25.7035 -3.4813 TD
[(Lemma)-250.1(2.1)]TJ
/TT4 1 Tf
5.277 0 TD
[(For)-250(every)-250.4(constituent)-250.8(tr)37.1(ee)]TJ
/F2 1 Tf
10.5718 0 TD
()Tj
/TT4 1 Tf
0.553 0 TD
(,)Tj
/F5 1 Tf
-1.3187 -1.0698 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 260.9873 232.3295 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
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0.13 Tc
[(\()130()10.1(\))]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 284.9843 243.3751 Tm
0 Tc
(2)Tj
/F1 1 Tf
6.9738 0 0 6.9738 289.9657 247.4897 Tm
()Tj
/TT4 1 Tf
0.848 0 TD
(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-40(\))]TJ
/F1 1 Tf
9.9626 0 0 9.9626 314.0693 243.3751 Tm
(=)Tj
/TT2 1 Tf
1.0577 0 TD
(1)Tj
/F2 1 Tf
0.5 0 TD
(.)Tj
/TT2 1 Tf
13.2786 0 TD
(\(10\))Tj
/TT4 1 Tf
-34.834 -4.0722 TD
[(Pr)37(oof.)]TJ
/F5 1 Tf
7.5964 -1.841 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 186.4 163.9539 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
0.13 Tc
[(\()130()10(\))]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 210.397 174.9994 Tm
0 Tc
(2)Tj
/F1 1 Tf
6.9738 0 0 6.9738 215.3783 179.114 Tm
()Tj
/TT4 1 Tf
0.848 0 TD
(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-40(\))]TJ
/F1 1 Tf
9.9626 0 0 9.9626 239.4819 174.9994 Tm
(=)Tj
/F5 1 Tf
1.1778 1.5678 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 261.6269 180.3075 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
0.13 Tc
[(\()130()10(\))]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 286.1221 183.1469 Tm
0 Tc
(2)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 291.5776 186.7634 Tm
(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-120(\))]TJ
/F1 1 Tf
1.299 0 TD
()Tj
/TT4 1 Tf
0.848 0 TD
(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-40(\))]TJ
ET
251.228 177.706 76.217 -0.458 re
f
BT
/TT2 1 Tf
9.9626 0 0 9.9626 279.0884 167.926 Tm
(2)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 284.544 170.8052 Tm
(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-119.8(\))]TJ
/F1 1 Tf
9.9626 0 0 9.9626 331.3963 174.9994 Tm
(=)Tj
/F5 1 Tf
1.1778 1.5678 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 353.5412 180.3075 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
0.13 Tc
[(\()130()10(\))]TJ
/F1 1 Tf
9.9626 0 0 9.9626 378.0364 183.1469 Tm
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/F2 1 Tf
0.629 0 TD
()Tj
/TT2 1 Tf
0.6639 0 TD
([)Tj
/F6 1 Tf
0.333 0 TD
(C)Tj
/TT4 1 Tf
4.9813 0 0 4.9813 251.7709 675.2456 Tm
(A)Tj
/TT2 1 Tf
6.9738 0 0 6.9738 255.4122 676.2916 Tm
(])Tj
9.9626 0 0 9.9626 259.3943 687.3123 Tm
(2)Tj
/F1 1 Tf
6.9738 0 0 6.9738 264.3756 691.4269 Tm
()Tj
/TT4 1 Tf
0.848 0 TD
(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-40(\))]TJ
/TT4 1 Tf
9.9626 0 0 9.9626 286.409 687.3123 Tm
(F)Tj
/F2 1 Tf
0.702 0 TD
[(\()-40(\))]TJ
/F1 1 Tf
1.6348 0 TD
(=)Tj
/F5 1 Tf
1.1885 0.95 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 320.2281 676.2916 Tm
()Tj
/F1 1 Tf
0.553 0 TD
()Tj
/F6 1 Tf
0.629 0 TD
(C)Tj
/TT4 1 Tf
4.9813 0 0 4.9813 333.2892 675.2456 Tm
(A)Tj
9.9626 0 0 9.9626 339.2887 687.3123 Tm
(F)Tj
/F2 1 Tf
0.702 0 TD
[(\()-119.9(\).)]TJ
/TT2 1 Tf
11.6029 0 TD
(\(18\))Tj
-34.834 -2.7089 TD
[(using)-219(applications)-219.9(of)-219(lemma)-219.7(2.1)-219(\(page)-219.3(7\).)-322.6(Let)]TJ
/F4 1 Tf
18.2974 0 TD
(C)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 303.0655 658.8301 Tm
(A)Tj
/F1 1 Tf
9.9626 0 0 9.9626 310.7318 660.3245 Tm
0.2778 Tc
(={)Tj
/F2 1 Tf
1.4278 0 TD
0 Tc
()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 329.2702 658.8301 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 333.2553 660.3245 Tm
0.1667 Tc
[(,...)-166.6(,)]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 362.3452 658.8301 Tm
0 Tc
(n)Tj
/F1 1 Tf
9.9626 0 0 9.9626 366.6441 660.3245 Tm
(})Tj
/TT2 1 Tf
0.37 0 TD
[(,)-225.2(and)-219.2(let)]TJ
/TT4 1 Tf
3.3802 0 TD
(T)Tj
/TT2 1 Tf
0.926 0 TD
(and)Tj
/TT4 1 Tf
1.685 0 TD
(g)Tj
/TT2 1 Tf
0.7569 0 TD
[(be)-219.1(de)]TJ
/TT7 1 Tf
2.1068 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
(ned)Tj
-35.056 -1.2 TD
[(as)-250(above.)-333.3(Then)]TJ
/F5 1 Tf
2.2534 -0.8494 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 131.1462 619.4229 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
()Tj
/TT2 1 Tf
0.664 0 TD
([)Tj
/F6 1 Tf
0.333 0 TD
(C)Tj
/TT4 1 Tf
4.9813 0 0 4.9813 151.5647 618.3768 Tm
(A)Tj
/TT2 1 Tf
6.9738 0 0 6.9738 155.206 619.4229 Tm
(])Tj
9.9626 0 0 9.9626 159.189 630.4426 Tm
(2)Tj
/F1 1 Tf
6.9738 0 0 6.9738 164.1704 634.5571 Tm
()Tj
/TT4 1 Tf
0.848 0 TD
(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-40(\))]TJ
/TT4 1 Tf
9.9626 0 0 9.9626 186.2038 630.4426 Tm
(F)Tj
/F2 1 Tf
0.702 0 TD
[(\()-40(\))]TJ
/F1 1 Tf
-5.2284 -3.4761 TD
(=)Tj
/F5 1 Tf
2.3966 0.95 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 158.8423 584.7917 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
()Tj
/TT2 1 Tf
0.664 0 TD
([)Tj
/F6 1 Tf
0.333 0 TD
(C)Tj
/TT4 1 Tf
4.9813 0 0 4.9813 179.2608 583.7457 Tm
(A)Tj
/TT2 1 Tf
6.9738 0 0 6.9738 182.9021 584.7917 Tm
(])Tj
/F5 1 Tf
9.9626 0 0 9.9626 186.8852 612.7878 Tm
()Tj
/TT2 1 Tf
0.693 -1.704 TD
(2)Tj
/F1 1 Tf
6.9738 0 0 6.9738 198.7706 599.926 Tm
()Tj
/TT4 1 Tf
0.848 0 TD
(N)Tj
/F2 1 Tf
0.783 0 TD
[(\()-40(\))]TJ
/F5 1 Tf
9.9626 0 0 9.9626 222.7726 605.2759 Tm
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 221.7664 584.7917 Tm
()Tj
/F1 1 Tf
0.553 0 TD
()Tj
/F6 1 Tf
0.629 0 TD
(C)Tj
/F2 1 Tf
4.9813 0 0 4.9813 234.3353 583.7457 Tm
()Tj
/TT4 1 Tf
9.9626 0 0 9.9626 240.2341 595.8114 Tm
(F)Tj
/F2 1 Tf
0.702 0 TD
[(\()-120(\))]TJ
/F5 1 Tf
1.299 1.704 TD
( )Tj
/F1 1 Tf
-11.9507 -5.1812 TD
(=)Tj
/F5 1 Tf
1.8269 0.95 TD
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 158.8423 549.517 Tm
(t)Tj
/F1 1 Tf
0.368 0 TD
()Tj
/TT4 1 Tf
0.652 0 TD
(T)Tj
/TT2 1 Tf
4.9813 0 0 4.9813 170.8862 551.5325 Tm
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 175.5358 578.1457 Tm
()Tj
1.0054 -0.754 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 182.4398 550.1238 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/TT4 1 Tf
0.651 0 TD
(g)Tj
/F2 1 Tf
0.538 0 TD
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
9.9626 0 0 9.9626 204.4214 561.1694 Tm
0.09 Tc
[(\()90()50(\))]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 231.3943 572.7369 Tm
0 Tc
(n)Tj
/F5 1 Tf
9.9626 0 0 9.9626 226.2466 570.6339 Tm
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 227.4999 550.1796 Tm
(i)Tj
/F1 1 Tf
0.375 0 TD
(=)Tj
/TT2 1 Tf
0.78 0 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 242.0035 561.1694 Tm
( )Tj
/TT4 1 Tf
6.9738 0 0 6.9738 247.9323 559.6749 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 251.0456 561.1694 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
/TT4 1 Tf
0.443 0 TD
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 277.8162 559.6749 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 280.9295 561.1694 Tm
(\))Tj
/F5 1 Tf
0.373 1.704 TD
( )Tj
/F1 1 Tf
0.9152 -1.704 TD
0.2223 Tc
[(+)55.7()55.6()0.1(+)]TJ
/F5 1 Tf
3.4522 0.95 TD
0 Tc
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 327.5766 550.2463 Tm
(t)Tj
/F1 1 Tf
0.368 0 TD
()Tj
/TT4 1 Tf
0.652 0 TD
(T)Tj
4.9813 0 0 4.9813 339.6204 552.2617 Tm
(n)Tj
/F5 1 Tf
9.9626 0 0 9.9626 344.4942 578.1457 Tm
()Tj
1.0054 -0.754 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 351.3983 550.1238 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/TT4 1 Tf
0.651 0 TD
(g)Tj
/F2 1 Tf
0.538 0 TD
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
9.9626 0 0 9.9626 373.3799 561.1694 Tm
0.09 Tc
[(\()90()50(\))]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 400.3527 572.7369 Tm
0 Tc
(n)Tj
/F5 1 Tf
9.9626 0 0 9.9626 395.205 570.6339 Tm
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 396.4583 550.1796 Tm
(i)Tj
/F1 1 Tf
0.375 0 TD
(=)Tj
/TT2 1 Tf
0.78 0 TD
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 410.9619 561.1694 Tm
( )Tj
/TT4 1 Tf
6.9738 0 0 6.9738 416.8907 559.6749 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 420.004 561.1694 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
/TT4 1 Tf
0.443 0 TD
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 446.7746 559.6749 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 449.8879 561.1694 Tm
(\))Tj
/F5 1 Tf
0.373 1.704 TD
( )Tj
/F1 1 Tf
-31.3667 -5.2148 TD
(=)Tj
/F5 1 Tf
1.8269 0.95 TD
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 158.8423 514.5402 Tm
(t)Tj
/F1 1 Tf
0.368 0 TD
()Tj
/TT4 1 Tf
0.652 0 TD
(T)Tj
/TT2 1 Tf
4.9813 0 0 4.9813 170.8862 516.5556 Tm
(1)Tj
/TT4 1 Tf
6.9738 0 0 6.9738 180.6834 537.7601 Tm
(n)Tj
/F5 1 Tf
9.9626 0 0 9.9626 175.5358 535.657 Tm
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 176.789 515.2028 Tm
(i)Tj
/F1 1 Tf
0.375 0 TD
(=)Tj
/TT2 1 Tf
0.78 0 TD
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 191.2927 543.1688 Tm
()Tj
/F2 1 Tf
0.693 -1.704 TD
( )Tj
/TT4 1 Tf
6.9738 0 0 6.9738 204.1255 524.6981 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 207.2389 526.1925 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
/TT4 1 Tf
0.443 0 TD
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 234.0095 524.6981 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 237.1228 526.1925 Tm
(\))Tj
/F5 1 Tf
0.8521 0.95 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 242.4996 515.1469 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/TT4 1 Tf
0.651 0 TD
(g)Tj
/F2 1 Tf
0.538 0 TD
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
9.9626 0 0 9.9626 264.4812 526.1925 Tm
0.09 Tc
[(\()90()50(\))]TJ
/F5 1 Tf
2.024 1.704 TD
0 Tc
( )Tj
/F1 1 Tf
0.9152 -1.704 TD
0.2223 Tc
[(+)55.7()55.6()0.1(+)]TJ
/F5 1 Tf
3.4522 0.95 TD
0 Tc
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 327.5766 515.2685 Tm
(t)Tj
/F1 1 Tf
0.368 0 TD
()Tj
/TT4 1 Tf
0.652 0 TD
(T)Tj
4.9813 0 0 4.9813 339.6204 517.2839 Tm
(n)Tj
6.9738 0 0 6.9738 349.6419 537.7601 Tm
(n)Tj
/F5 1 Tf
9.9626 0 0 9.9626 344.4942 535.657 Tm
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 345.7475 515.2028 Tm
(i)Tj
/F1 1 Tf
0.375 0 TD
(=)Tj
/TT2 1 Tf
0.78 0 TD
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 360.2511 543.1688 Tm
()Tj
/F2 1 Tf
0.693 -1.704 TD
( )Tj
/TT4 1 Tf
6.9738 0 0 6.9738 373.084 524.6981 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 376.1973 526.1925 Tm
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
/TT4 1 Tf
0.443 0 TD
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 402.9679 524.6981 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 406.0812 526.1925 Tm
(\))Tj
/F5 1 Tf
0.8521 0.95 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 411.458 515.1469 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/TT4 1 Tf
0.651 0 TD
(g)Tj
/F2 1 Tf
0.538 0 TD
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
9.9626 0 0 9.9626 433.4396 526.1925 Tm
0.09 Tc
[(\()90()50(\))]TJ
/F5 1 Tf
2.024 1.704 TD
0 Tc
( )Tj
/F1 1 Tf
-31.3667 -5.2149 TD
(=)Tj
/TT4 1 Tf
1.85 0 TD
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 174.5634 489.7203 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 178.5484 491.2147 Tm
(\))Tj
/F5 1 Tf
0.5397 1.704 TD
()Tj
1.026 -0.754 TD
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 190.8294 480.1691 Tm
(t)Tj
/F1 1 Tf
0.368 0 TD
()Tj
/TT4 1 Tf
0.652 0 TD
(T)Tj
/F2 1 Tf
0.707 0 TD
(\()Tj
/TT2 1 Tf
0.373 0 TD
(1)Tj
/F2 1 Tf
0.5 0 TD
(\))Tj
/F5 1 Tf
9.9626 0 0 9.9626 216.3348 500.6792 Tm
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 213.2224 480.1691 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/TT4 1 Tf
0.651 0 TD
(g)Tj
/F2 1 Tf
0.538 0 TD
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
9.9626 0 0 9.9626 235.205 491.2147 Tm
0.09 Tc
[(\()90()50(\))]TJ
/F5 1 Tf
2.024 1.704 TD
0 Tc
( )Tj
/F1 1 Tf
0.9152 -1.704 TD
0.2222 Tc
[(+)55.5()55.6()0(+)]TJ
/TT4 1 Tf
3.464 0 TD
0 Tc
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 314.0214 489.7203 Tm
(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 318.3203 491.2147 Tm
(\))Tj
/F5 1 Tf
0.5396 1.704 TD
()Tj
1.0418 -0.754 TD
()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 330.6003 480.1691 Tm
(t)Tj
/F1 1 Tf
0.368 0 TD
()Tj
/TT4 1 Tf
0.652 0 TD
(T)Tj
/F2 1 Tf
0.707 0 TD
(\()Tj
/TT4 1 Tf
0.373 0 TD
(n)Tj
/F2 1 Tf
0.545 0 TD
(\))Tj
/F5 1 Tf
9.9626 0 0 9.9626 356.4204 500.6792 Tm
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 353.3081 480.1691 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/TT4 1 Tf
0.651 0 TD
(g)Tj
/F2 1 Tf
0.538 0 TD
(\()Tj
/TT4 1 Tf
0.373 0 TD
(t)Tj
/F2 1 Tf
0.368 0 TD
(\))Tj
9.9626 0 0 9.9626 375.2897 491.2147 Tm
0.09 Tc
[(\()90()50(\))]TJ
/F5 1 Tf
2.024 1.704 TD
0 Tc
( )Tj
/F1 1 Tf
-25.5299 -4.4148 TD
(=)Tj
/TT4 1 Tf
1.85 0 TD
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 174.5634 462.7135 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 178.5484 464.2079 Tm
(\))Tj
/F5 1 Tf
1.3869 0.95 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 183.9253 453.1624 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/TT4 1 Tf
0.651 0 TD
(g)Tj
/TT2 1 Tf
0.538 0 TD
([)Tj
/TT4 1 Tf
0.3559 0 TD
(T)Tj
/F2 1 Tf
0.707 0 TD
(\()Tj
/TT2 1 Tf
0.373 0 TD
(1)Tj
/F2 1 Tf
0.5 0 TD
(\))Tj
/TT2 1 Tf
0.373 0 TD
(])Tj
/F2 1 Tf
9.9626 0 0 9.9626 216.5629 464.2079 Tm
0.09 Tc
[(\()90()50(\))]TJ
/F1 1 Tf
3.2462 0 TD
0.1667 Tc
[(+)-1055.5()-1055.5(+)]TJ
/TT4 1 Tf
6.464 0 TD
0 Tc
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 328.3258 462.7135 Tm
(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 332.6247 464.2079 Tm
(\))Tj
/F5 1 Tf
1.4026 0.95 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 338.0005 453.1624 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/TT4 1 Tf
0.651 0 TD
(g)Tj
/TT2 1 Tf
0.538 0 TD
([)Tj
/TT4 1 Tf
0.356 0 TD
(T)Tj
/F2 1 Tf
0.707 0 TD
(\()Tj
/TT4 1 Tf
0.373 0 TD
(n)Tj
/F2 1 Tf
0.545 0 TD
(\))Tj
/TT2 1 Tf
0.373 0 TD
(])Tj
/F2 1 Tf
9.9626 0 0 9.9626 370.9529 464.2079 Tm
0.09 Tc
[(\()90()50(\))]TJ
/F1 1 Tf
-23.0706 -2.7108 TD
0 Tc
(=)Tj
/TT4 1 Tf
1.85 0 TD
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT2 1 Tf
6.9738 0 0 6.9738 174.5634 435.7068 Tm
(1)Tj
/F2 1 Tf
9.9626 0 0 9.9626 178.5484 437.2012 Tm
(\))Tj
/F5 1 Tf
1.0612 0.95 TD
()Tj
/F2 1 Tf
6.9738 0 0 6.9738 183.9253 426.1557 Tm
()Tj
/F1 1 Tf
0.611 0 TD
()Tj
/F2 1 Tf
0.629 0 TD
0.13 Tc
[(\()130()]TJ
/TT2 1 Tf
4.9813 0 0 4.9813 202.8244 425.1096 Tm
0 Tc
(1)Tj
/F2 1 Tf
6.9738 0 0 6.9738 205.8132 426.1557 Tm
(\))Tj
9.9626 0 0 9.9626 210.0742 437.2012 Tm
0.09 Tc
[(\()90()50(\))]TJ
/F1 1 Tf
3.2462 0 TD
0.1667 Tc
[(+)-1055.5()-1055.5(+)]TJ
/TT4 1 Tf
6.464 0 TD
0 Tc
(F)Tj
/F2 1 Tf
0.702 0 TD
(\()Tj
/TT4 1 Tf
6.9738 0 0 6.9738 321.8371 435.7068 Tm
(n)Tj
/F2 1 Tf
9.9626 0 0 9.9626 326.136 437.2012 Tm
(\))Tj
/F5 1 Tf
1.0725 0.95 TD
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/TT2 1 Tf
0.47 0 TD
(8)Tj
-26.0348 -1.2222 TD
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(DOP)Tj
8.9664 0 0 8.9664 237.5701 664.9901 Tm
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/TT2 1 Tf
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(81)Tj
/F2 1 Tf
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/TT2 1 Tf
0.47 0 TD
(8)Tj
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(DOP)Tj
8.9664 0 0 8.9664 235.3285 654.0311 Tm
0 Tc
(1)Tj
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(/)Tj
/TT2 1 Tf
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[(12)-1111.1(1)]TJ
/F2 1 Tf
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/TT2 1 Tf
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[(12)-1111.1(1)]TJ
/F2 1 Tf
2.6111 0 TD
(/)Tj
/TT2 1 Tf
0.47 0 TD
[(12)-1111.1(1)]TJ
/F2 1 Tf
2.6111 0 TD
(/)Tj
/TT2 1 Tf
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[(12)-1111.1(1)]TJ
/F2 1 Tf
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(/)Tj
/TT2 1 Tf
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1.1111 Tc
(61)Tj
/F2 1 Tf
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(61)Tj
/F2 1 Tf
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/TT2 1 Tf
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(61)Tj
/F2 1 Tf
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(6)Tj
ET
159.878 650.757 273.536 -0.199 re
f
BT
9.9626 0 0 9.9626 156.3756 619.1619 Tm
[(Figure)-250.1(3:)-333.2(Relative)-251(frequencies)-250.5(and)-250.2(probabilities)-250.9(of)-250(the)-250.3(trees)-250.3(in)]TJ
/TT7 1 Tf
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()Tj
/TT2 1 Tf
0.5562 0 TD
[(gure)-249.9(2)]TJ
-29.8041 -3.087 TD
[(constraint)-283.2(the)-283(new)]TJ
7.9701 0 0 7.9701 191.6015 588.4072 Tm
0.0616 Tc
(DOP)Tj
9.9626 0 0 9.9626 211.5836 588.4072 Tm
0 Tc
[(model)-283.2(is)-282.6(always)-282.8(equivalent)-283.6(to)-282.9(a)]TJ
7.9701 0 0 7.9701 341.6259 588.4072 Tm
0.0614 Tc
(PCFG)Tj
9.9626 0 0 9.9626 366.0912 588.4072 Tm
0 Tc
[(model,)-291.3(for)-282.7(any)-282.9(choice)-283.3(of)]TJ
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(G)Tj
/TT2 1 Tf
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(.)Tj
-36.25 -1.2 TD
(Let)Tj
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()Tj
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(have)Tj
/TT4 1 Tf
2.1625 0 TD
(n)Tj
/TT2 1 Tf
0.8196 0 TD
[(possible)-274.6(derivations)]TJ
/TT4 1 Tf
8.2709 0 TD
(d)Tj
/TT2 1 Tf
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(1)Tj
/F2 1 Tf
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0.1667 Tc
[(,...)-166.6(,)]TJ
/TT4 1 Tf
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0 Tc
(d)Tj
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(n)Tj
/TT2 1 Tf
9.9626 0 0 9.9626 294.2317 576.452 Tm
[(.)-406.5(Each)-275.1(derivation)]TJ
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/TT2 1 Tf
9.9626 0 0 9.9626 378.5355 576.452 Tm
[(consists)-274.5(of)]TJ
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/TT2 1 Tf
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0.2223 Tc
[( )55.7()55.6()0.1( )]TJ
/F2 1 Tf
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0 Tc
()Tj
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(m)Tj
4.9813 0 0 4.9813 193.5273 561.9564 Tm
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6.9738 0 0 6.9738 197.0421 563.0024 Tm
(j)Tj
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9.9626 0 0 9.9626 202.93 564.4968 Tm
(=)Tj
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1.0578 0 TD
()Tj
/TT2 1 Tf
0.553 0 TD
[(.)-333(Then,)]TJ
/TT4 1 Tf
-5.4039 -2.9971 TD
(P)Tj
/F2 1 Tf
0.693 0 TD
[(\()-120(\))]TJ
/F1 1 Tf
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()Tj
/TT4 1 Tf
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(N)Tj
/F2 1 Tf
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[(\()-120(\))]TJ
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()Tj
/TT4 1 Tf
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/F1 1 Tf
0.376 0 TD
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/TT4 1 Tf
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(f)Tj
/F2 1 Tf
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/TT4 1 Tf
6.9738 0 0 6.9738 279.4929 540.1273 Tm
(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 282.6062 541.6216 Tm
(\))Tj
ET
257.108 537.346 35.254 -0.458 re
f
BT
/TT4 1 Tf
9.9626 0 0 9.9626 259.3026 527.5644 Tm
(f)Tj
/F2 1 Tf
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/TT4 1 Tf
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(r)Tj
/F2 1 Tf
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(i)Tj
/F2 1 Tf
9.9626 0 0 9.9626 284.9425 527.5644 Tm
(\)\))Tj
/TT2 1 Tf
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[(by)-250(\(9\))]TJ
/F1 1 Tf
-20.2848 -3.4581 TD
(=)Tj
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[(\()-120(\))]TJ
/TT4 1 Tf
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9.9626 0 0 9.9626 225.865 509.6505 Tm
()Tj
/TT4 1 Tf
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(j)Tj
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(m)Tj
4.9813 0 0 4.9813 249.8899 511.8194 Tm
(j)Tj
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()Tj
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(i)Tj
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()Tj
/F2 1 Tf
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(\()Tj
/TT4 1 Tf
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(A)Tj
/F1 1 Tf
0.631 0 TD
()Tj
/F2 1 Tf
1.099 0 TD
0.04 Tc
(\))Tj
/F1 1 Tf
0.984 0 TD
0 Tc
()Tj
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0.648 0 TD
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(p)Tj
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0.531 0 TD
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/TT4 1 Tf
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(A)Tj
/F1 1 Tf
0.9087 0 TD
()Tj
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(\))Tj
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0 Tc
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(A)Tj
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(;)Tj
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(\))Tj
/TT2 1 Tf
9.9626 0 0 9.9626 389.8431 500.1861 Tm
[(by)-250(\(21\))]TJ
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-20.2848 -3.3464 TD
(=)Tj
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()Tj
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[(\()-120(\))]TJ
/TT4 1 Tf
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(n)Tj
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()Tj
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(j)Tj
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(=)Tj
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(1)Tj
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()Tj
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(A)Tj
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()Tj
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()Tj
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(p)Tj
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(A)Tj
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()Tj
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0 Tc
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(A)Tj
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(;)Tj
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(\))Tj
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0 Tc
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()Tj
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(\()Tj
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(p)Tj
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(A)Tj
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(\))Tj
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0 Tc
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(A)Tj
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(;)Tj
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(\))Tj
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0 Tc
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(2)Tj
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(N)Tj
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[(\()-120(\))]TJ
/TT2 1 Tf
9.9626 0 0 9.9626 114.8394 410.4097 Tm
[(Figure)-304.2(3)-304(shows)-303.5(that)-304.5(the)-304.3(former)]TJ
7.9701 0 0 7.9701 243.3873 410.4097 Tm
0.0616 Tc
(DOP)Tj
9.9626 0 0 9.9626 263.5816 410.4097 Tm
0 Tc
[(model)-304.5(assigns)-303.8(a)-304.2(probability)-304.8(to)-304.2(binary)-304.3(branching)-304.5(trees)]TJ
-14.93 -1.2 TD
[(that)-304.8(is)-304.3(twice)-304.7(as)-304.3(high)-304.5(as)-304.3(the)-304.6(probability)-305(assigned)-304.5(to)-304.4(the)-304.6(unary)-304.4(branching)-304.8(ones.)-495.9(In)-304.3(this)-304.4(case,)]TJ
T*
[(these)-241.2(probabilities)-241.8(are)-241.1(clearly)-241.7(wrong.)-329.7(In)-240.9(the)-241.2(next)-241.2(example)-241.6(we)-240.9(will)-241.1(see)-241(how)-240.7(the)-241.2(three)-241.3(models)]TJ
T*
[(behave)-250.5(if)-250.2(we)-250(drop)-250(the)-250.2(independence)-250.9(constraint.)]TJ
0 -1.7355 TD
[(T)69.8(ake)-232.6(the)-232.6(trees)-232.5(in)]TJ
/TT7 1 Tf
6.7461 0 TD
()Tj
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0.5562 0 TD
[(gure)-232.3(2,)-235.8(with)-232.5(their)-232.8(relative)-233.2(frequencies)-232.9(as)-232.2(given)-232.6(in)]TJ
/TT7 1 Tf
19.6728 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(gure)-232.3(3.)-327.1(W)79.8(e)-232.4(construct)-232.7(a)]TJ
-27.5313 -1.2 TD
[(new)-264.4(corpus,)-268(by)-264.4(taking)-264.9(all)-264.9(instances)-264.9(of)-264.4(tree)-264.9(\(2\),)-268(and)-264.6(swapping)-264.4(their)]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 382.3891 343.8044 Tm
(A)Tj
/F2 1 Tf
9.9626 0 0 9.9626 387.2877 345.2989 Tm
(\()Tj
/TT2 1 Tf
0.373 0 TD
(1)Tj
/F2 1 Tf
0.5 0 TD
(\))Tj
/TT2 1 Tf
0.6374 0 TD
[(with)-264.6(the)]TJ
/TT4 1 Tf
6.9738 0 0 6.9738 438.1818 343.8044 Tm
(A)Tj
/F2 1 Tf
9.9626 0 0 9.9626 443.0804 345.2989 Tm
(\()Tj
/TT2 1 Tf
0.373 0 TD
(0)Tj
/F2 1 Tf
0.5 0 TD
(\))Tj
/TT2 1 Tf
0.6374 0 TD
[(in)-264.6(all)]TJ
-34.4576 -1.2 TD
[(instances)-268.8(of)-268.4(tree)-268.9(\(5\).)-388.1(This)-268.6(action)-269(causes)-268.4(tree)-268.9(\(2\))-268.4(to)-268.5(become)-269(equal)-268.9(to)-268.5(tree)-268.9(\(1\),)-273(and)-268.6(tree)-268.8(\(5\))-268.4(to)]TJ
T*
[(become)-218.8(equal)-218.6(to)-218.4(tree)-218.7(\(7\).)-322.3(Our)-218(new)-218.2(corpus)-218.2(now)-217.9(consists)-218.2(only)-218.3(of)-218.2(instances)-218.6(of)-218.2(the)-218.5(6)-218.2(trees)-218.4(given)]TJ
T*
(in)Tj
/TT7 1 Tf
1.028 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
[(gure)-250(4,)-250(whose)-249.8(relative)-250.9(frequencies)-250.5(are)-250.3(given)-250.3(in)]TJ
/TT7 1 Tf
18.9106 0 TD
()Tj
/TT2 1 Tf
0.5562 0 TD
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