Symbolic Polytopes for Quantitative Interpolation and Verification - PowerPoint PPT Presentation

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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 Kpf, IMDEA Verification Quantitative verification Quantitative

Symbolic Polytopes for Quantitative Interpolation and Verification Klaus v. Gleissenthall, TU Munich joint work with Andrey Rybalchenko, Microsoft Research and Boris Köpf, IMDEA
Verification
Quantitative verification
Quantitative reachability property
This talk  Constraint solving problem  Quantitative interpolation  Symbolic polytopes and generating functions
Program as formula int ¡v; ¡ ¡ main(int ¡k) ¡{ ¡ ¡ ¡ ¡init(v,k); ¡ ¡ ¡ ¡while ¡(1) ¡step(v); ¡ ¡ } ¡
Quantitative verification is a logic problem
Simple yet expressive
Unfold, guess, and check Bounded problem Recursion check 9
Bounded problem is interpolation [Craig’57, McMillan’03]
Interpolants as polytopes  Integer points represented by linear inequalities  Model for numeric data types
Generating functions
Decomposition [Brion’88, Barvinok’93]
Quantitative interpolation w/o size
Evaluation
Find h: generating recursive bounded functions

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