Axiomatizing NFAs Generated by Regular Grammars

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 6 axioms plus 2 conditional axioms, only.