Symbolic Polytopes for Quantitative Verification

Klaus von Gleissenthall

14th May 2015 (Thursday), 10:00 in KE322


Proving quantitative properties of programs, such as bounds on resource usage or information leakage, often leads to verification conditions that involve cardinalities of sets. Existing approaches for dealing with such verification conditions operate by checking cardinality bounds for given formulas. However, they cannot synthesize formulas that satisfy given cardinality constraints, which limits their applicability for inferring cardinality-based inductive arguments.
This talk presents a novel algorithm for synthesizing formulas for given cardinality constraints, which relies on the theory of counting integral points in symbolic polytopes. The algorithm is cast in terms of a cardinality-constrained interpolation procedure, which is put to work in a solver for recursive Horn clauses with cardinality constraints based on abstraction refinement. I will conclude with an experimental evaluation on a number of representative examples.

The talk is based on joint work with Boris Köpf and Andrey Rybalchenko.

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