Equation solving using modal transition systems

Abstract

This research offers as its main contribution a complete treatment of equation solving within process algebra for equation systems of the following form: C/sub 1/(X) approximately P/sub 1/, . . ., C/sub n(X)/ approximately P/sub n/ where C/sub i/ are arbitrary contexts (i.e. derived operators) of some process algebra, P/sub i/ are arbitrary process (i.e. terms of the process algebra), approximately is the bisimulation equivalence, and X is the unknown process to be found (if possible). It is shown that the solution set to this equation may be characterized in terms of a distinctive modal transition system, and that a solution to the above equation systems may be readily extracted (when solutions exist) on this basis. In fact, the results have led to an implementation (in Prolog) of an automatic tool for solving equations in the finite-state case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>