Probabilistic Grammars and Languages

Authors:
András Kornai
Affiliations:
Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary 1111 and Institute for Quantitative Social Science, Harvard University, Cambridge, USA 02138
Venue:
Journal of Logic, Language and Information
Year:
2011

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Abstract

Using an asymptotic characterization of probabilistic finite state languages over a one-letter alphabet we construct a probabilistic language with regular support that cannot be generated by probabilistic CFGs. Since all probability values used in the example are rational, our work is immune to the criticism leveled by Suppes (Synthese 22:95---116, 1970) against the work of Ellis (1969) who first constructed probabilistic FSLs that admit no probabilistic FSGs. Some implications for probabilistic language modeling by HMMs are discussed.