Abstract
We present a novel framework to reason about programs based on encodings of computations as graphs. The main insight here is to rearrange the programs such that given a bound k, each computation can be explored according to any tree decomposition of width k of the corresponding behaviour graph. This produces under-approximations parameterized on k, which result in a complete method when we restrict to classes of behaviour graphs of bounded tree-width. As an additional feature, the transformation of the input program can be targeted to existing tools for the analysis. Thus, off-the-shelf tools based on fixed-point, or capable of analyzing sequential programs with scalar variables and nondeterminism, can be used. To illustrate our approach, we develop this framework for sequential programs and discuss how to extend it to handle concurrency. For the case of sequential programs, we develop a compositional approach to generate on-the-fly tree decompositions of nested words, which is based on graph-summaries.
This work was partially supported by INDAM-GNCS 2022 and 2023, AWS 2021 Amazon Research Awards, the MUR project ‘Innovation, digitalisation and sustainability for the diffused economy in Central Italy’, Spoke 1 MEGHALITIC, VITALITY Ecosystem, and FARB 2021–2023 grants Università degli Studi di Salerno.
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Notes
- 1.
We assume that there are no unmatched calls and returns, differently from [1].
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Inverso, O., La Torre, S., Parlato, G., Tomasco, E. (2023). Verifying Programs by Bounded Tree-Width Behavior Graphs. In: Malvone, V., Murano, A. (eds) Multi-Agent Systems. EUMAS 2023. Lecture Notes in Computer Science(), vol 14282. Springer, Cham. https://doi.org/10.1007/978-3-031-43264-4_8
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