Deciding Synchronous Kleene Algebra with Derivatives

Abstract

Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come to a halt. The synchronous Kleene algebra with tests (SKAT) combines SKA with a Boolean algebra. Both algebras were introduced by Prisacariu, who proved the decidability of the equational theory, through a Kleene theorem based on the classical Thompson -NFA construction. Using the notion of partial derivatives, we present a new decision procedure for equivalence between SKA terms. The results are extended for SKAT considering automata with transitions labeled by Boolean expressions instead of atoms. This work continous previous research done for KA and KAT, where derivative based methods were used in feasible algorithms for testing terms equivalence. (c) Springer International Publishing Switzerland 2015.