Abstract

SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition relation of a system, while employing SMT-based procedures, such as interpolation, to mitigate the limitations of local reasoning and allow for better generalization. Unfortunately, these mitigations intertwine model checking with heuristics of the underlying SMT-solver, negatively affecting stability of model checking. In this paper, we propose to tackle the limitations of locality in a systematic manner. We introduce explicit global guidance into the local reasoning performed by IC3-style algorithms. To this end, we extend the SMT-IC3 paradigm with three novel rules, designed to mitigate fundamental sources of failure that stem from locality. We instantiate these rules for the theory of Linear Integer Arithmetic and implement them on top of Spacer solver in Z3. Our empirical results show that GSpacer, Spacer extended with global guidance, is significantly more effective than both Spacer and sole global reasoning, and, furthermore, is insensitive to interpolation.

Highlights

  • SMT-based Model Checking algorithms that combine SMT-based search for bounded counterexamples with interpolation-based search for inductive invariants are currently the most effective techniques for verification of infinite state systems

  • We present a novel approach that extends, what we call, local reasoning of IC3-style algorithms with global guidance inspired by the invariant inference algorithms described above

  • We propose an efficient instantiation of the rules for the theory Linear Integer Arithmetic

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Summary

Introduction

SMT-based Model Checking algorithms that combine SMT-based search for bounded counterexamples with interpolation-based search for inductive invariants are currently the most effective techniques for verification of infinite state systems. The Achilles heel of these approaches is the mismatch between the local reasoning used to establish absence of bounded counterexamples and a global reason for absence of unbounded counterexamples (i.e., existence of an inductive invariant) This is apparent in IC3-style algorithms [7], such as Spacer [18]. IC3-style algorithms establish bounded safety by repeatedly computing predecessors of error (or bad) states, blocking them by local reasoning c The Author(s) 2020 S. We present a novel approach that extends, what we call, local reasoning of IC3-style algorithms with global guidance inspired by the invariant inference algorithms described above. Spacer always attempts to compute the most general predecessor states This is the best local strategy, but blocking these regions by learning their negation leads to the aforementioned lemmas.

Background
Global Guidance of Local Proofs
Global Guidance for Linear Integer Arithmetic
Lemma Selection
Subsume Rule for LIA
Concretize Rule for LIA
Conjecture Rule for LIA
Evaluation
Related Work
Conclusion and Future Work
Full Text
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