The Generalized Smallest Grammar Problem

Payam Siyari, Matthias Gallé
Proceedings of The 13th International Conference on Grammatical Inference, PMLR 57:79-92, 2017.

Abstract

The Smallest Grammar Problem – the problem of finding the smallest context-free grammar that generates exactly one given sequence – has never been successfully applied to grammatical inference. We investigate the reasons and propose an extended formulation that seeks to minimize non-recursive grammars, instead of straight-line programs. In addition, we provide very efficient algorithms that approximate the minimization problem of this class of grammars. Our empirical evaluation shows that we are able to find smaller models than the current best approximations to the Smallest Grammar Problem on standard benchmarks, and that the inferred rules capture much better the syntactic structure of natural language.

Cite this Paper

BibTeX
@InProceedings{pmlr-v57-siyari16, title = {The Generalized Smallest Grammar Problem}, author = {Siyari, Payam and Gallé, Matthias}, booktitle = {Proceedings of The 13th International Conference on Grammatical Inference}, pages = {79--92}, year = {2017}, editor = {Verwer, Sicco and Zaanen, Menno van and Smetsers, Rick}, volume = {57}, series = {Proceedings of Machine Learning Research}, address = {Delft, The Netherlands}, month = {05--07 Oct}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v57/siyari16.pdf}, url = {http://proceedings.mlr.press/v57/siyari16.html}, abstract = {The Smallest Grammar Problem – the problem of finding the smallest context-free grammar that generates exactly one given sequence – has never been successfully applied to grammatical inference. We investigate the reasons and propose an extended formulation that seeks to minimize non-recursive grammars, instead of straight-line programs. In addition, we provide very efficient algorithms that approximate the minimization problem of this class of grammars. Our empirical evaluation shows that we are able to find smaller models than the current best approximations to the Smallest Grammar Problem on standard benchmarks, and that the inferred rules capture much better the syntactic structure of natural language.} }
Endnote
%0 Conference Paper %T The Generalized Smallest Grammar Problem %A Payam Siyari %A Matthias Gallé %B Proceedings of The 13th International Conference on Grammatical Inference %C Proceedings of Machine Learning Research %D 2017 %E Sicco Verwer %E Menno van Zaanen %E Rick Smetsers %F pmlr-v57-siyari16 %I PMLR %P 79--92 %U http://proceedings.mlr.press/v57/siyari16.html %V 57 %X The Smallest Grammar Problem – the problem of finding the smallest context-free grammar that generates exactly one given sequence – has never been successfully applied to grammatical inference. We investigate the reasons and propose an extended formulation that seeks to minimize non-recursive grammars, instead of straight-line programs. In addition, we provide very efficient algorithms that approximate the minimization problem of this class of grammars. Our empirical evaluation shows that we are able to find smaller models than the current best approximations to the Smallest Grammar Problem on standard benchmarks, and that the inferred rules capture much better the syntactic structure of natural language.
RIS
TY - CPAPER TI - The Generalized Smallest Grammar Problem AU - Payam Siyari AU - Matthias Gallé BT - Proceedings of The 13th International Conference on Grammatical Inference DA - 2017/01/16 ED - Sicco Verwer ED - Menno van Zaanen ED - Rick Smetsers ID - pmlr-v57-siyari16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 57 SP - 79 EP - 92 L1 - http://proceedings.mlr.press/v57/siyari16.pdf UR - http://proceedings.mlr.press/v57/siyari16.html AB - The Smallest Grammar Problem – the problem of finding the smallest context-free grammar that generates exactly one given sequence – has never been successfully applied to grammatical inference. We investigate the reasons and propose an extended formulation that seeks to minimize non-recursive grammars, instead of straight-line programs. In addition, we provide very efficient algorithms that approximate the minimization problem of this class of grammars. Our empirical evaluation shows that we are able to find smaller models than the current best approximations to the Smallest Grammar Problem on standard benchmarks, and that the inferred rules capture much better the syntactic structure of natural language. ER -
APA
Siyari, P. & Gallé, M.. (2017). The Generalized Smallest Grammar Problem. Proceedings of The 13th International Conference on Grammatical Inference, in Proceedings of Machine Learning Research 57:79-92 Available from http://proceedings.mlr.press/v57/siyari16.html.

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