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Symbolic Computation in Automated Program Reasoning

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Formal Methods (FM 2023)

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We describe applications of symbolic computation towards automating the formal analysis of while-programs implementing polynomial arithmetic. We combine methods from static analysis, symbolic summation and computer algebra to derive polynomial loop invariants, yielding a finite representation of all polynomial equations that are valid before and after each loop execution. While deriving polynomial invariants is in general undecidable, we identify classes of loops for which we automatically can solve the problem of invariant synthesis. We further generalize our work to the analysis of probabilistic program loops. Doing so, we compute higher-order statistical moments over (random) program variables, inferring this way quantitative invariants of probabilistic program loops. Our results yield computer-aided solutions in support of formal software verification, compiler optimization, and probabilistic reasoning.

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  1. 1.

    As we focus now only on invariant synthesis, we set true to be the loop condition of Fig. 2.


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The work described in this talk is based on joint works with a number of authors, including Daneshvar Amrollahi (TU Wien alumni), Ezio Bartocci (TU Wien), Andreas Humenberger (TU Wien alumni), Maximillian Jaroschek (TU Wien alumni), Tudor Jebelean (RISC-Linz), George Kenison (TU Wien), Marcel Moosbrugger (TU Wien), and Miroslav Stankovic (TU Wien).

The author acknowledges funding and support from the ERC Consolidator Grant 2020 ARTIST 101002685, the ProbInG grant of the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19018], the Austrian FWF project W1255-N23, and the SecInt Doctoral College funded by TU Wien.

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Correspondence to Laura Kovács .

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Kovács, L. (2023). Symbolic Computation in Automated Program Reasoning. In: Chechik, M., Katoen, JP., Leucker, M. (eds) Formal Methods. FM 2023. Lecture Notes in Computer Science, vol 14000. Springer, Cham.

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