Towards automatic temporal logic verification of value passing process algebra using abstract interpretation

In this paper we present an abstract model of process semantics, Abstract Trace Semantics, which is built on top of an abstract interpretation for (the Abstract Data Types part of) LOT08. We use it as a model for an abstract interpretation of a linear time temporal logics. Both Abstract Trace Semantics and the abstract interpretation of the aatisfiability relation are proven correct w.r.t. their concrete counterparts. The main advantage of the proposed approach is that it makes automatic model checking applicable also to full value passing process algebras. Currently, model checking is applied only to process algebraic specifications where only synchronization is supported (or, equivalently, value passing is restricted to data types which must be finite). By means of abstract interpretation we can reduce the infinite branching of labeled transition systems, which is due to infinite data types, to finite branching. In this way we can completely automate the verification that a formula is satisfied by a process in the abstract domain, When the formula is satisfied by the process in the abstract domain, then the correctness theorem guarantees that indeed the formula holds for the process.