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Probabilistic Context-Free Grammars

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Encyclopedia of Machine Learning

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Synonyms

PCFG

Definition

In formal language theory, formal grammar (phrase-structure grammar) is developed to capture the generative process of languages (Hopcroft & Ullman, 1979). A formal grammar is a set of productions (rewriting rules) that are used to generate a set of strings, that is, a language. The productions are applied iteratively to generate a string, a process called derivation. The simplest kind of formal grammar is a regular grammar.

Context-free grammars (CFG) form a more powerful class of formal grammars than regular grammars and are often used to define the syntax of programming languages. Formally, a CFG consists of a set of nonterminal symbols N, a terminal alphabet Σ, a set P of productions (rewriting rules), and a special nonterminal S called the start symbol. For a nonempty set X of symbols, let X * denote the set of all finite strings of symbols in X. Every CFG production has the form S → α, where S ∈ N and α ∈ (N ∪Σ)*. That is, the left-hand side consists of...

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Recommended Reading

  • Durbin, R., Eddy, S., Krogh, A., & Mitchison, G. (1998). Biological sequence analysis. Cambridge, UK: Cambridge University Press.

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  • Hopcroft, J. E., & Ullman, J. D. (1979). Introduction to automata theory, languages and computation. Reading, MA: Addison-Wesley.

    MATH  Google Scholar 

  • Lari, K., & Young, S. J. (1990). The estimation of stochastic context-free grammars using the inside-outside algorithm. Computer Speech and Language, 4, 35–56.

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  • Sakakibara, Y. (1997). Recent advances of grammatical inference. Theoretical Computer Science, 185, 15–45.

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  • Sakakibara, Y. (2005). Grammatical inference in bioinformatics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 1051–1062.

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Author information

Authors and Affiliations

  1. sKeio University, Hiyoshi, Kohoku-ku, Japan

    Yasubumi Sakakibara

Authors
  1. Yasubumi Sakakibara
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Editor information

Editors and Affiliations

  1. School of Computer Science and Engineering, University of New South Wales, Sydney, Australia, 2052

    Claude Sammut

  2. Faculty of Information Technology, Clayton School of Information Technology, Monash University, P.O. Box 63, Victoria, Australia, 3800

    Geoffrey I. Webb

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Sakakibara, Y. (2011). Probabilistic Context-Free Grammars. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30164-8_669

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