On Complete Systems and Finite Automata

On Complete Systems and Finite Automata

A production on T* is a rewriting rule σα→σ' for all aϵ T*, where σ, σ' are strings in T* with a' lexicographically earlier than σ. Any finite collection of productions is called a system. This note shows that any system that is consistent, complete, and has the nonprefix property uni...

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Bibliographic Details
Published in:IEEE transactions on computers Vol. C-21; no. 10; pp. 1109 - 1113
Main Author: Pu, A.T.
Format: Journal Article
Language:English
Published: IEEE 01-10-1972
Subjects:
Complete system
consistent system
nonprefix property
reduced string
reduced system
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Summary:A production on T* is a rewriting rule σα→σ' for all aϵ T*, where σ, σ' are strings in T* with a' lexicographically earlier than σ. Any finite collection of productions is called a system. This note shows that any system that is consistent, complete, and has the nonprefix property uniquely represents an automaton. This formulation characterizes automata as recognition devices in terms of a set of rewriting rules, similar to the characterizatibn of automata as generating devices by grammars.
ISSN:0018-9340
1557-9956
DOI:10.1109/T-C.1972.223457