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arXiv · 2402.00502

Axiomatizing NFAs Generated by Regular Grammars

Roberto Gorrieri
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Abstract

A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA $N$, there exists a process algebraic term $p$ such that its semantics is a GFA isomorphic to $N$. Moreover, we provide a concise axiomatization of language equivalence: two GFAs $N_1$ and $N_2$ recognize the same regular language if and only if the associated terms $p_1$ and $p_2$, respectively, can be equated by means of a set of axioms, comprising 7 axioms plus 2 conditional axioms, only.

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Roberto Gorrieri. 2024-02-01. Axiomatizing NFAs Generated by Regular Grammars. https://arxiv.org/abs/2402.00502

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