Robustness of the Random Language Model

The Random Language Model (De Giuli 2019) is an ensemble of stochastic context-free grammars, quantifying the syntax of human and computer languages. The model suggests a simple picture of first language learning as a type of annealing in the vast space of potential languages. In its simplest formulation, it implies a single continuous transition to grammatical syntax, at which the symmetry among potential words and categories is spontaneously broken. Here this picture is scrutinized by considering its robustness against explicit symmetry breaking, an inevitable component of learning in the real world. It is shown that the scenario is robust to such symmetry breaking. Comparison with human data on the clustering coefficient of syntax networks suggests that the observed transition is equivalent to that normally experienced by children at age 24 months

Quantum, Stochastic, and Pseudo Stochastic Languages with Few States

Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all these numbers of states are optimal. After this, we completely characterize the class of languages recognized by 1-state GFAs, which is the only nontrivial class of languages recognized by 1-state automata. Finally, we consider the variations of PFAs, QFAs, and GFAs based on the notion of inclusive/exclusive cutpoint, and present some results on their expressive power.Comment: A new version with new results. Previous version: Arseny M. Shur, Abuzer Yakaryilmaz: Quantum, Stochastic, and Pseudo Stochastic Languages with Few States. UCNC 2014: 327-33

Computation of moments for probabilistic finite-state automata

[EN] The computation of moments of probabilistic finite-state automata (PFA) is researched in this article. First, the computation of moments of the length of the paths is introduced for general PFA, and then, the computation of moments of the number of times that a symbol appears in the strings generated by the PFA is described. These computations require a matrix inversion. Acyclic PFA, such as word graphs, are quite common in many practical applications. Algorithms for the efficient computation of the moments for acyclic PFA are also presented in this paper.This work has been partially supported by the Ministerio de Ciencia y Tecnologia under the grant TIN2017-91452-EXP (IBEM), by the Generalitat Valenciana under the grant PROMETE0/2019/121 (DeepPattern), and by the grant "Ayudas Fundacion BBVA a equipos de investigacion cientifica 2018" (PR[8]_HUM_C2_0087).Sánchez Peiró, JA.; Romero, V. (2020). Computation of moments for probabilistic finite-state automata. Information Sciences. 516:388-400. https://doi.org/10.1016/j.ins.2019.12.052S388400516Sakakibara, Y., Brown, M., Hughey, R., Mian, I. S., Sjölander, K., Underwood, R. C., & Haussler, D. (1994). Stochastic context-free grammers for tRNA modeling. Nucleic Acids Research, 22(23), 5112-5120. doi:10.1093/nar/22.23.5112Álvaro, F., Sánchez, J.-A., & Benedí, J.-M. (2016). An integrated grammar-based approach for mathematical expression recognition. Pattern Recognition, 51, 135-147. doi:10.1016/j.patcog.2015.09.013Mohri, M., Pereira, F., & Riley, M. (2002). Weighted finite-state transducers in speech recognition. Computer Speech & Language, 16(1), 69-88. doi:10.1006/csla.2001.0184Casacuberta, F., & Vidal, E. (2004). Machine Translation with Inferred Stochastic Finite-State Transducers. Computational Linguistics, 30(2), 205-225. doi:10.1162/089120104323093294Ortmanns, S., Ney, H., & Aubert, X. (1997). A word graph algorithm for large vocabulary continuous speech recognition. Computer Speech & Language, 11(1), 43-72. doi:10.1006/csla.1996.0022Soule, S. (1974). Entropies of probabilistic grammars. Information and Control, 25(1), 57-74. doi:10.1016/s0019-9958(74)90799-2Justesen, J., & Larsen, K. J. (1975). On probabilistic context-free grammars that achieve capacity. Information and Control, 29(3), 268-285. doi:10.1016/s0019-9958(75)90437-4Hernando, D., Crespi, V., & Cybenko, G. (2005). Efficient Computation of the Hidden Markov Model Entropy for a Given Observation Sequence. IEEE Transactions on Information Theory, 51(7), 2681-2685. doi:10.1109/tit.2005.850223Nederhof, M.-J., & Satta, G. (2008). Computation of distances for regular and context-free probabilistic languages. Theoretical Computer Science, 395(2-3), 235-254. doi:10.1016/j.tcs.2008.01.010CORTES, C., MOHRI, M., RASTOGI, A., & RILEY, M. (2008). ON THE COMPUTATION OF THE RELATIVE ENTROPY OF PROBABILISTIC AUTOMATA. International Journal of Foundations of Computer Science, 19(01), 219-242. doi:10.1142/s0129054108005644Ilic, V. M., Stankovi, M. S., & Todorovic, B. T. (2011). Entropy Message Passing. IEEE Transactions on Information Theory, 57(1), 375-380. doi:10.1109/tit.2010.2090235Booth, T. L., & Thompson, R. A. (1973). Applying Probability Measures to Abstract Languages. IEEE Transactions on Computers, C-22(5), 442-450. doi:10.1109/t-c.1973.223746Thompson, R. A. (1974). Determination of Probabilistic Grammars for Functionally Specified Probability-Measure Languages. IEEE Transactions on Computers, C-23(6), 603-614. doi:10.1109/t-c.1974.224001Wetherell, C. S. (1980). Probabilistic Languages: A Review and Some Open Questions. ACM Computing Surveys, 12(4), 361-379. doi:10.1145/356827.356829Sanchez, J.-A., & Benedi, J.-M. (1997). Consistency of stochastic context-free grammars from probabilistic estimation based on growth transformations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(9), 1052-1055. doi:10.1109/34.615455Hutchins, S. E. (1972). Moments of string and derivation lengths of stochastic context-free grammars. Information Sciences, 4(2), 179-191. doi:10.1016/0020-0255(72)90011-4Heim, A., Sidorenko, V., & Sorger, U. (2008). Computation of distributions and their moments in the trellis. Advances in Mathematics of Communications, 2(4), 373-391. doi:10.3934/amc.2008.2.373Vidal, E., Thollard, F., de la Higuera, C., Casacuberta, F., & Carrasco, R. C. (2005). Probabilistic finite-state machines - part I. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(7), 1013-1025. doi:10.1109/tpami.2005.147Sánchez, J. A., Rocha, M. A., Romero, V., & Villegas, M. (2018). On the Derivational Entropy of Left-to-Right Probabilistic Finite-State Automata and Hidden Markov Models. Computational Linguistics, 44(1), 17-37. doi:10.1162/coli_a_0030

Weakly Restricted Stochastic Grammars

A new type of stochastic grammars is introduced for investigation: weakly restricted stochastic grammars. In this paper we will concentrate on the consistency problem. To find conditions for stochastic grammars to be consistent, the theory of multitype Galton-Watson branching processes and generating functions is of central importance.\ud The unrestricted stochastic grammar formalism generates the same class of languages as the weakly restricted formalism. The inside-outside algorithm is adapted for use with weakly restricted grammars

Parametrized Stochastic Grammars for RNA Secondary Structure Prediction

We propose a two-level stochastic context-free grammar (SCFG) architecture for parametrized stochastic modeling of a family of RNA sequences, including their secondary structure. A stochastic model of this type can be used for maximum a posteriori estimation of the secondary structure of any new sequence in the family. The proposed SCFG architecture models RNA subsequences comprising paired bases as stochastically weighted Dyck-language words, i.e., as weighted balanced-parenthesis expressions. The length of each run of unpaired bases, forming a loop or a bulge, is taken to have a phase-type distribution: that of the hitting time in a finite-state Markov chain. Without loss of generality, each such Markov chain can be taken to have a bounded complexity. The scheme yields an overall family SCFG with a manageable number of parameters.Comment: 5 pages, submitted to the 2007 Information Theory and Applications Workshop (ITA 2007

Probabilistic parsing

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