Claude Michel

Alexandre Goldsztejn, Claude Michel, Michel Rueher

This paper introduces a new algorithm for solving a sub-class of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has numerous applications in engineering and design. We propose here a new generic branch and prune algorithm for solving such continuous QCSPs. Standard pruning operators and solution identification operators are specialized for universally quantified inequalities. Special rules are also proposed for handling the parameters of the constraints. First experimentation show that our algorithm outperforms the state of the art methods.

Heytem Zitoun, Claude Michel, Laurent Michel et al.

Program verification techniques typically focus on finding counter-examples that violate properties of a program. Constraint programming offers a convenient way to verify programs by modeling their state transformations and specifying searches that seek counter-examples. Floating-point computations present additional challenges for verification given the semantic subtleties of floating point arithmetic. % This paper focuses on search strategies for CSPs using floating point numbers constraint systems and dedicated to program verification. It introduces a new search heuristic based on the global number of occurrences that outperforms state-of-the-art strategies. More importantly, it demonstrates that a new technique that only branches on input variables of the verified program improve performance. It composes with a diversification technique that prevents the selection of the same variable within a fixed horizon further improving performances and reduces disparities between various variable choice heuristics. The result is a robust methodology that can tailor the search strategy according to the sought properties of the counter example.

Hélène Collavizza, Claude Michel, Michel Rueher

Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the path corresponding to the same computation with real numbers. A common practice when validating such programs consists in estimating the accuracy of floating-point computations with respect to the same sequence of operations in an ide-alized semantics of real numbers. However, state-of-the-art tools compute an over-approximation of the error introduced by floating-point operations. As a consequence, totally inappropriate behaviors of a program may be dreaded but the developer does not know whether these behaviors will actually occur, or not. In this paper, we introduce a new constraint-based approach that searches for test cases in the part of the over-approximation where errors due to floating-point arithmetic would lead to inappropriate behaviors.