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Finite state languages
Open accessAbstract
A finite state language is a finite or infinite set of strings (sentences) of symbols (words) generated by a finite set of rules (the grammar), where each rule specifies the state of the system in which it can be applied, the symbol which is generated, and the state of the system after the rule is applied. A number of equivalent descriptions of finite state languages are explored. A simple structural characterization theorem for finite state languages is established, based on the cyclical structure of the grammar. It is shown that the complement of any finite state language formed on a given vocabulary of symbols is also a finite state language, and that the union of any two finite state languages formed on a given vocabulary is a finite state language; i.e., the set of all finite state languages that can be formed on a given vocabulary is a Boolean algebra. Procedures for calculating the number of grammatical strings of any given length are also described.
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Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
Cited by
The faculty of language: what is it, who has it, and how did it evolve?
Hauser, M. D., Chomsky, N., & Fitch, W. T. (2002) · Science · doi:10.1126/science.298.5598.1569 · Cited by 5,189
Self-citationImplicit learning of artificial grammars
Reber, A. S. (1967) · Journal of Verbal Learning and Verbal Behavior · doi:10.1016/s0022-5371(67)80149-x · Cited by 2,026
Implicit learning of synthetic languages: The role of instructional set.
Reber, A. S. (1976) · Journal of Experimental Psychology: Human Learning and Memory · doi:10.1037/0278-7393.2.1.88 · Cited by 523
Metadata
- Authors
- Chomsky, N., & Miller, G. A.
- Venue
- Information and Control
- Publisher
- Elsevier BV
- Published
- 1958-05
- Volume
- 1
- Issue
- 2
- Pages
- 91-112
- ISSN
- 0019-9958 (ISSN-L)
- OpenAlex
- W2017473312
- Cited by
- 383
- References
- 1
- FWCI
- 8.55
- Type
- journal article
- Language
- en
- Open access
- bronze
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