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Incremental Property Directed Reachability

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Formal Methods and Software Engineering (ICFEM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14308))

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Abstract

Property Directed Reachability (PDR) is a widely used technique for formal verification of hardware and software systems. This paper presents an incremental version of PDR (IPDR), which enables the automatic verification of system instances of incremental complexity. The proposed algorithm leverages the concept of incremental SAT solvers to reuse verification results from previously verified system instances, thereby accelerating the verification process. The new algorithm supports both incremental constraining and relaxing; i.e., starting from an over-constrained instance that is gradually relaxed.

To validate the effectiveness of the proposed algorithm, we implemented IPDR and experimentally evaluate it on two different problem domains. First, we consider a circuit pebbling problem, where the number of pebbles is both constrained and relaxed. Second, we explore parallel program instances, progressively increasing the allowed number of interleavings. The experimental results demonstrate significant performance improvements compared to Z3’s PDR implementation SPACER. Experiments also show that the incremental approach succeeds in reusing a substantial amount of clauses between instances, for both the constraining and relaxing algorithm.

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Notes

  1. 1.

    Without loss of generality, we may assume that \(\overline{P}\) is a single state (i.e., a sink state).

  2. 2.

    This represents for instance the scenario when we find the minimum number of pebbles to successfully pebble a circuit by approximating the pebble count from above; reducing pebbles in each run until goal of pebbling the circuit is no longer possible.

  3. 3.

    This represents for instance the scenario when we find a bug after increasing the number of interleavings in a parallel program.

  4. 4.

    https://github.com/Majeux/pebbling-pdr.

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Authors and Affiliations

  1. Leiden University, Leiden Institute for Advanced Computer Science, Leiden, The Netherlands

    Max Blankestijn & Alfons Laarman

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  1. Max Blankestijn
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  2. Alfons Laarman
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Correspondence to Alfons Laarman .

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  1. Nanyang Technological University, Singapore, Singapore

    Yi Li

  2. Concordia University, Montreal, QC, Canada

    Sofiène Tahar

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Blankestijn, M., Laarman, A. (2023). Incremental Property Directed Reachability. In: Li, Y., Tahar, S. (eds) Formal Methods and Software Engineering. ICFEM 2023. Lecture Notes in Computer Science, vol 14308. Springer, Singapore. https://doi.org/10.1007/978-981-99-7584-6_13

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