The Algebra of Nondeterministic Finite Automata

Abstract

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.