Symbolic Polytopes for Quantitative Interpolation and Verification - PowerPoint PPT Presentation

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 ž Constraint solving problem ž Quantitative interpolation ž 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 ž Integer points represented by linear inequalities ž Model for numeric data types

Generating functions

Decomposition [Brion’88, Barvinok’93]

Quantitative interpolation w/o size

Evaluation

Find h: generating recursive bounded functions