Equations and regular-like expressions for afa

Abstract

lternating finite automata are a generalization of non-deterministic finite automata and a mechanism that models parallel computation. It has been shown in [6] that alternating finite automata (AFA) have several theoretical properties and practical features. In this paper, we further study alternating finite automata. A new type of system of equations is introduced. The systems of equations to be considered involve Boolean expressions over a finite set X and the symbols of an alphabet A. Each AFA can be described as a system of equations that has a unique fixpoint, and whose solutions are precisely the regular languages. We present an algebraic interpretation of AFA, which parallels that of regular expressions and of linear equations. We also explore direct ways of solving such systems and generating equivalent AFA from regular expressions or even extended regular expressions.