In Representation of Events in Nerve Nets and Finite Automata , S. C. Kleene obtains a number of interesting results. The most important of these, his analysis and synthesis theorems (theorems 5 and 3), are obscured both by the complexity of his basic concepts and by the nature of the elements used in his nets. In this paper we give a new formulation and new proofs of Kleene’s analysis and synthesis theorems, in which we presuppose no acquaintance with Kleene’s work. We use simpler basic concepts and construct our nets out of more familiar and convenient elements (see section 4). The simplified formulation and proofs should make these important results more widely accessible. Some detailed comments on Kleene’s ideas are made in section 7.
KeywordsInput Sequence Regular Expression Input State Transition Sequence Finite Sequence
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