Hyperproperty Verification as CHC Satisfiability
Author:
Itzhaky Shachar,Shoham Sharon,Vizel Yakir
Abstract
AbstractHyperproperties specify the behavior of a system across multiple executions, and are an important extension of regular temporal properties. So far, such properties have resisted comprehensive treatment by software model-checking approaches such as IC3/PDR, due to the need to find not only an inductive invariant but also a total alignment of different executions that facilitates simpler inductive invariants.We show how this treatment is achieved via a reduction from the verification problem of $$\forall ^*\exists ^*$$
∀
∗
∃
∗
hyperproperties to Constrained Horn Clauses (CHCs). Our starting point is a set of universally quantified formulas in first-order logic (modulo theories) that encode the verification of $$\forall ^*\exists ^*$$
∀
∗
∃
∗
hyperproperties over infinite-state transition systems. The first-order encoding uses uninterpreted predicates to capture the (1) witness function for existential quantification over traces, (2) alignment of executions, and (3) corresponding inductive invariant. Such an encoding was previously proposed for k-safety properties. Unfortunately, finding a satisfying model for the resulting first-order formulas is beyond reach for modern first-order satisfiability solvers. Previous works tackled this obstacle by developing specialized solvers for the aforementioned first-order formulas. In contrast, we show that the same problems can be encoded as CHCs and solved by existing CHC solvers. CHC solvers take advantage of the unique structure of CHC formulas and handle the combination of quantifiers with theories and uninterpreted predicates more efficiently.Our key technical contribution is a logical transformation of the aforementioned sets of first-order formulas to equi-satisfiable sets of CHCs. The transformation to CHCs is sound and complete, and applying it to the first-order formulas that encode verification of hyperproperties leads to a CHC encoding of these problems. We implemented the CHC encoding in a prototype tool and show that, using existing CHC solvers for solving the CHCs, the approach already outperforms state-of-the-art tools for hyperproperty verification by orders of magnitude.
Publisher
Springer Nature Switzerland
Reference49 articles.
1. Antonopoulos, T., Koskinen, E., Le, T. C., Nagasamudram, R., Naumann, D. A., and Ngo, M. An algebra of alignment for relational verification. Proc. ACM Program. Lang. 7, POPL (jan 2023). 2. Baier, C., Coenen, N., Finkbeiner, B., Funke, F., Jantsch, S., and Siber, J. Causality-based game solving. In Computer Aided Verification - 33rd International Conference, CAV 2021, Virtual Event, July 20-23, 2021, Proceedings, Part I (2021), A. Silva and K. R. M. Leino, Eds., vol. 12759 of Lecture Notes in Computer Science, Springer, pp. 894–917. 3. Barthe, G., Crespo, J. M., and Kunz, C. Relational verification using product programs. In FM 2011: Formal Methods - 17th International Symposium on Formal Methods, Limerick, Ireland, June 20-24, 2011. Proceedings (2011), pp. 200–214. 4. Barthe, G., Crespo, J. M., and Kunz, C. Beyond 2-safety: Asymmetric product programs for relational program verification. In Logical Foundations of Computer Science, International Symposium, LFCS 2013, San Diego, CA, USA, January 6-8, 2013. Proceedings (2013), S. N. Artëmov and A. Nerode, Eds., vol. 7734 of Lecture Notes in Computer Science, Springer, pp. 29–43. 5. Barthe, G., D’Argenio, P. R., and Rezk, T. Secure information flow by self-composition. In 17th IEEE Computer Security Foundations Workshop, (CSFW-17 2004), 28-30 June 2004, Pacific Grove, CA, USA (2004), pp. 100–114.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
|
|