Issue No.10 - October (1972 vol.21)
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.
Complete system, consistent system, nonprefix property, reduced string, reduced system.
A.T. Pu, "On Complete Systems and Finite Automata", IEEE Transactions on Computers, vol.21, no. 10, pp. 1109-1113, October 1972, doi:10.1109/T-C.1972.223457