SMT-based verification of data-aware processes: a model-theoretic approach

Abstract

In recent times, satisfiability modulo theories (SMT) techniques gained increasing attention and obtained remarkable success in model-checking infinite-state systems. Still, we believe that whenever more expressivity is needed in order to specify the systems to be verified, more and more support is needed from mathematical logic and model theory. This is the case of the applications considered in this paper: we study verification over a general model of relational, data-aware processes, to assess (parameterized) safety properties irrespectively of the initial database (DB) instance. Toward this goal, we take inspiration from array-based systems and tackle safety algorithmically via backward reachability. To enable the adoption of this technique in our rich setting, we make use of the model-theoretic machinery of model completion, which surprisingly turns out to be an effective tool for verification of relational systems and represents the main original contribution of this paper. In this way, we pursue a twofold purpose. On the one hand, we isolate three notable classes for which backward reachability terminates, in turn witnessing decidability. Two of such classes relate our approach to conditions singled out in the literature, whereas the third one is genuinely novel. On the other hand, we are able to exploit SMT technology in implementations, building on the well-known MCMT (Model Checker Modulo Theories) model checker for array-based systems and extending it to make all our foundational results fully operational. All in all, the present contribution is deeply rooted in the long-standing tradition of the application of model theory in computer science. In particular, this paper applies these ideas in an original mathematical context and shows how these techniques can be used for the first time to empower algorithmic techniques for the verification of infinite-state systems based on arrays, so as to make such techniques applicable to the timely, challenging settings of data-aware processes.

Model Completeness, Uniform Interpolants and Superposition Calculus

“…The usefulness of covers in model checking was already stressed in [37] and further motivated by our recent line of research on the verification of data-aware processes (also called 'database driven applications' in this paper) [12,13,15,17]. Notably, this is also operationally mirrored in the MCMT model checker [32] starting from version 2.8 (database driven module).…”

“…Let M be a model of T . By using a chain argument [17] (see [18], Lemma 3.5.7 for an almost identical construction), we show that there exists a model M of T such that M embeds into M .…”

“…In this section we supply old and new motivations for investigating covers and model completions in view of model-checking applications. We first report the considerations from [11,13,17,37] on symbolic model-checking via model completions (or, equivalently, via covers) in the basic case where system variables are represented as individual variables; for more advanced applications where system variables are both individual and higher order variables, see [11,13,17]. Similar ideas (i.e., 'to use quantifier elimination in the model completion even if T does not allow quantifier elimination') were used in [59] for interpolation and symbol elimination.…”

“…4.1 below) precisely uses signatures comprising unary function symbols and free n-ary relations. In [11,13,17] we apply model completeness techniques for verifying transition systems based on read-only databases, in a framework where such systems employ both individual and higher order variables.…”

“…Then, in Sect. 4 we report our applications (mostly taken from [17]) concerning verification of data-aware processes. We begin the second part of the paper by proving (Sect.…”