Equational Abstractions in Rewriting Logic and Maude

Abstract

Maude is a high-level language and high-performance system supporting both equational and rewriting computation for a wide range of applications. Maude also provides a model checker for linear temporal logic. The model-checking procedure can be used to prove properties when the set of states reachable from an initial state in a system is finite; when this is not the case, it may be possible to use an equational abstraction technique for reducing the size of the state space. Abstraction reduces the problem of whether an infinite state system satisfies a temporal logic property to model checking that property on a finite state abstract version of the original infinite system. The most common abstractions are quotients of the original system. We present a simple method for defining quotient abstractions by means of equations identifying states. Our method yields the minimal quotient system together with a set of proof obligations that guarantee its executability, which can be discharged with tools such as those available in the Maude formal environment. The proposed method will be illustrated by means of detailed examples.

Research supported by MINECO Spanish projects StrongSoft (TIN2012–39391–C04–04) and TIN2011–23795, and Comunidad de Madrid program N-GREENS Software (S2013/ICE-2731).