3-Valued abstraction: More precision at less cost

AbstractThis paper investigates both the precision and the model checking efficiency of abstract models designed to preserve branching time logics w.r.t. a 3-valued semantics. Current abstract models use ordinary transitions to over approximate the concrete transitions, while they use hyper transitions to under approximate the concrete transitions. In this work, we refer to precision measured w.r.t. the choice of abstract states, independently of the formalism used to describe abstract models. We show that current abstract models do not allow maximal precision. We suggest a new class of models and a construction of an abstract model which is most precise w.r.t. any choice of abstract states. As before, the construction of such models might involve an exponential blowup, which is inherent by the use of hyper transitions. We therefore suggest an efficient algorithm in which the abstract model is constructed during model checking, by need. Our algorithm achieves maximal precision w.r.t. the given property while remaining quadratic in the number of abstract states. To complete the picture, we incorporate it into an abstraction-refinement framework

An Infinite Needle in a Finite Haystack: Finding Infinite Counter-Models in Deductive Verification

First-order logic, and quantifiers in particular, are widely used in deductive verification. Quantifiers are essential for describing systems with unbounded domains, but prove difficult for automated solvers. Significant effort has been dedicated to finding quantifier instantiations that establish unsatisfiability, thus ensuring validity of a system's verification conditions. However, in many cases the formulas are satisfiable: this is often the case in intermediate steps of the verification process. For such cases, existing tools are limited to finding finite models as counterexamples. Yet, some quantified formulas are satisfiable but only have infinite models. Such infinite counter-models are especially typical when first-order logic is used to approximate inductive definitions such as linked lists or the natural numbers. The inability of solvers to find infinite models makes them diverge in these cases. In this paper, we tackle the problem of finding such infinite models. These models allow the user to identify and fix bugs in the modeling of the system and its properties. Our approach consists of three parts. First, we introduce symbolic structures as a way to represent certain infinite models. Second, we describe an effective model finding procedure that symbolically explores a given family of symbolic structures. Finally, we identify a new decidable fragment of first-order logic that extends and subsumes the many-sorted variant of EPR, where satisfiable formulas always have a model representable by a symbolic structure within a known family. We evaluate our approach on examples from the domains of distributed consensus protocols and of heap-manipulating programs. Our implementation quickly finds infinite counter-models that demonstrate the source of verification failures in a simple way, while SMT solvers and theorem provers such as Z3, cvc5, and Vampire diverge

State Merging with Quantifiers in Symbolic Execution

We address the problem of constraint encoding explosion which hinders the applicability of state merging in symbolic execution. Specifically, our goal is to reduce the number of disjunctions and if-then-else expressions introduced during state merging. The main idea is to dynamically partition the symbolic states into merging groups according to a similar uniform structure detected in their path constraints, which allows to efficiently encode the merged path constraint and memory using quantifiers. To address the added complexity of solving quantified constraints, we propose a specialized solving procedure that reduces the solving time in many cases. Our evaluation shows that our approach can lead to significant performance gains