Progressive Solutions to FSM Equations

Abstract

The equation solving problem is to derive the behavior of the unknown component X knowing the joint behavior of the other components (or the context) C and the specification of the overall system S. The component X can be derived by solving the Finite State Machine (FSM) equation C $\lozenge$ X ~ S, where $\lozenge$ is the parallel composition operator and ~ is the trace equivalence or the trace reduction relation. A solution X to an FSM equation is called progressive if for every external input sequence the composition C $\lozenge$ X does not fall into a livelock without an exit. In this paper, we formally define the notion of a progressive solution to a parallel FSM equation and present an algorithm that derives a largest progressive solution (if a progressive solution exists). In addition, we generalize the work to a system of FSM equations. Application examples are provided.