The Algebra of Nondeterministic Finite Automata

TL;DR

This paper introduces a process algebra that precisely models nondeterministic finite automata (NFA), providing a representation theorem and a concise axiomatization for language equivalence.

Contribution

It establishes a formal correspondence between process algebra terms and NFAs, offering a new algebraic framework for analyzing automata.

Findings

Existence of a process algebraic term for each NFA

A concise set of axioms characterizes language equivalence

Representation theorem linking process algebra and NFAs

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.