Exploiting Over- and Under-Approximations for Infinite-State Counterpart Models

Abstract

Abstract. Software systems with dynamic topology are often infinitestate. Paradigmatic examples are those modeled as graph transformation systems (GTSs) with rewrite rules that allow an unbounded creation of items. For such systems, verification can become intractable, thus calling for the development of approximation techniques that may ease the verification at the cost of losing in preciseness and completeness. Both over-and under-approximations have been considered in the literature, respectively offering more and less behaviors than the original system. At the same time, properties of the system may be either preserved or reflected by a given approximation. In this paper we propose a general notion of approximation that captures some of the existing approaches for GTSs. Formulae are specified by a generic quantified modal logic, one that also generalizes many specification logics adopted in the literature for GTSs. We also propose a type system to denote part of the formulae as either reflected or preserved, together with a technique that exploits under-and over-approximations to reason about typed as well as untyped formulae.

Specification and Verification of Modal Properties for Structured Systems

“…Finally, [9] proposes a general formalization of similarity-based counterpart model approximations, and a technique for approximated verification exploiting them. We extended and generalized in several directions the type system of [4], proposed within the unfolding technique to classify formulae as preserved or reflected by a given approximation: (i) our type system is technique-agnostic, meaning that it does not require a particular approximation technique; (ii) we consider counterpart models, a generalization of GTrSs; (iii) our type system is parametric with respect to a given simulation relation (while the original one considers only those with certain properties); (iv) we use the type system to reason on all formulae (rather than just on closed ones); and (v) we propose a technique that exploits approximations to estimate properties more precisely, handling also part of the untyped formulae.…”