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Encyclopedia of Machine Learning and Data Mining pp 1013–1017Cite as

Probabilistic Context-Free Grammars

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PCFG

Definition

In formal language theory, formal grammar (phrase-structure grammar) is developed to capture the generative process of languages (Hopcroft and 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 \(\alpha \in (N \cup \Sigma )^{{\ast}}\). That is,...

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Recommended Reading

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

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  • Hopcroft JE, Ullman JD (1979) Introduction to automata theory, languages and computation. Addison-Wesley, Reading

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  • Lari K, Young SJ (1990) The estimation of stochastic context-free grammars using the inside-outside algorithm. Comput Speech Lang 4:35–56

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  • Sakakibara Y (1997) Recent advances of grammatical inference. Theor Comput Sci 185:15–45

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  • Sakakibara Y (2005) Grammatical inference in bioinformatics. IEEE Trans Pattern Anal Mach Intell 27:1051–1062

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Author information

Authors and Affiliations

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

    Yasubumi Sakakibara

Authors
  1. Yasubumi Sakakibara
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Editor information

Editors and Affiliations

  1. The University of New South Wales, Sydney, NSW, Australia

    Claude Sammut

  2. Faculty of Information Technology, Monash University, Melbourne, VIC, Australia

    Geoffrey I. Webb

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Sakakibara, Y. (2017). Probabilistic Context-Free Grammars. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_669

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