The Formal Complexity of Natural Language pp 41-55 | Cite as
An Elementary Proof of the Peters-Ritchie Theorem
Chapter
Abstract
The mathematical results about various classes of transformational grammars continue to play a role in linguistic discussions. Peters and Ritchie (1973a) proved that transformational grammars of the “standard” sort with a context-sensitive base were equivalent to unrestricted rewriting systems (equivalently, Turing machines) in their weak generative capacity, that is, that there was such a grammar for every recursively enumerable language. The proof can be presented informally and is easy to grasp (see Bach, 1974, for an informal presentation of the proof).
Keywords
Turing Machine Deep Structure Informal Presentation Transformational Grammar Blocking Symbol
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References
- Bach, Emmon (1974). Syntactic Theory. New York.Google Scholar
- Chomsky, Noam (1973). ‘Conditions on Transformations.’ In Stephen R. Anderson and Paul Kiparsky, eds., A Festschrift for Moris Halls.Google Scholar
- Cullicover, Peter and Kenneth Wexler (1977). ‘Some Syntactic Implications of a Theory of Language Learnability.’ In P. W. Culicover, T. Wasow, and A. Akmajian: eds., Formal Syntax. New York.Google Scholar
- Davis, Martin (1968). Computability and Unsolvability.. New York.Google Scholar
- Hamburger, Henry and Kenneth N. Wexler (1973). ‘Identifiability of a Class of Transformational Grammars.’ In K. J. J. Hintikka, J. M. E. Moravcsik, and P. Suppes, eds., Approaches to Natural Language. Dordrecht.Google Scholar
- Peters, P. S., Jr. and R. W. Ritchie (1971). ‘On Restricting the Base Component of Transformational Grammars.’ Information and Control, 18: 483–501.MathSciNetMATHCrossRefGoogle Scholar
- Peters, Stanley and R. W. Ritchie (1973a). ‘On the Generative Power of Transformational Grammars.’ Information Science, 6: 49–83.MathSciNetCrossRefGoogle Scholar
- Peters, P. Stanley Jr., and R. W. Ritchie (1973b). ‘Nonfiltering and Local-filtering Transformational Grammars.’ In K. J. Hintikka, J. M. E. Moravcsik, and P. Suppes, eds., Approaches to Natural Language. Dordrecht.Google Scholar
Copyright information
© D. Reidel Publishing Company, Dordrecht, Holland 1987