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On Complete Systems and Finite Automata
October 1972 (vol. 21 no. 10)
pp. 1109-1113
A.T. Pu, Department of Mathematics, Northern Michigan University
A production on T* is a rewriting rule sa?s' for all a? T*, where s, s' are strings in T* with a' lexicographically earlier than s. 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.
Index Terms:
Complete system, consistent system, nonprefix property, reduced string, reduced system.
Citation:
A.T. Pu, "On Complete Systems and Finite Automata," IEEE Transactions on Computers, vol. 21, no. 10, pp. 1109-1113, Oct. 1972, doi:10.1109/T-C.1972.223457
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