Symbolic Polytopes for Quantitative Interpolation and Verification - - PowerPoint PPT Presentation

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Jan 24, 2024 428 likes •599 views

Symbolic Polytopes for Quantitative Interpolation and Verification Klaus v. Gleissenthall, TU Munich joint work with Andrey Rybalchenko, Microsoft Research and Boris Kpf, IMDEA Verification Quantitative verification Quantitative

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Symbolic Polytopes for Quantitative Interpolation and Verification

Klaus v. Gleissenthall, TU Munich joint work with Andrey Rybalchenko, Microsoft Research and Boris Köpf, IMDEA

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Verification

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Quantitative verification

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Quantitative reachability property

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This talk

 Constraint solving problem  Quantitative interpolation  Symbolic polytopes and

generating functions

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Program as formula

int ¡v; ¡ ¡ main(int ¡k) ¡{ ¡ ¡ ¡ ¡init(v,k); ¡ ¡ ¡ ¡while ¡(1) ¡step(v); ¡ ¡ } ¡

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Quantitative verification is a logic problem

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Simple yet expressive

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Unfold, guess, and check

Bounded problem Recursion check

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Bounded problem is interpolation

[Craig’57, McMillan’03]

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Interpolants as polytopes

 Integer points represented by linear inequalities  Model for numeric data types

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Generating functions

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Decomposition [Brion’88, Barvinok’93]

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Quantitative interpolation w/o size

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Evaluation

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Find h:

recursive bounded generating functions