An Afficient Equivalence-Checking Algorithm for a Model of Programs with Commutative and Absorptive Statements

We present an efficient equivalence-checking algorithm for a propositional model of programs with semantics based on (what we call) progressive monoids on the finite set of statements generated by relations of a specific form. We consider arbitrary set of relations for commutativity (relations of the form ab = ba for statements a, b) and left absorption (relations of the form ab = b for statements a, b) properties. The main results are a polynomial-time decidability for the equivalence problem in the considered case, and an explicit description of an equivalence-checking algorithm which terminates in time polynomial in size