The Algebra of Nondeterministic Finite Automata

01/09/2023

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by   Roberto Gorrieri, et al.

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A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA N, there exists a process algebraic term p such that its semantics is an NFA isomorphic to N. Moreover, we provide a concise axiomatization of language equivalence: two NFAs N_1 and N_2 recognize the same 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 3 conditional axioms, only.