Exploiting over- and under-approximations for infinite-state counterpart models

Software systems with dynamic topology are often infinite-state. 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 quantied modal logic that 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.