Encyclopedia of Machine Learning

2010 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Probabilistic Context-Free Grammars

  • Yasubumi Sakakibara
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30164-8_669




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 SN and α ∈ (NΣ)*. That is, the left-hand side consists of...

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Recommended Reading

  1. Durbin, R., Eddy, S., Krogh, A., & Mitchison, G. (1998). Biological sequence analysis. Cambridge, UK: Cambridge University Press.MATHCrossRefGoogle Scholar
  2. Hopcroft, J. E., & Ullman, J. D. (1979). Introduction to automata theory, languages and computation. Reading, MA: Addison-Wesley.MATHGoogle Scholar
  3. 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.CrossRefGoogle Scholar
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  5. Sakakibara, Y. (2005). Grammatical inference in bioinformatics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 1051–1062.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Yasubumi Sakakibara
    • 1
  1. 1.sKeio UniversityHiyoshiJapan