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

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