[hal-01094787] The Power of Polynomials

Every component in the program development chain uses a model to represent and reason about its source. The model must be as expressive as possible without compromising its efficiency and tractability. This paper proposes a slight extension to the polyhedral model by allowing polynomial constraints and relations. Recent mathematical results by Handelman and Schweighofer on the Positivstellensatz allow one to devise algorithms similar to familiar emptiness tests or the Farkas algorithm. This paper presents applications of these ideas to three use-cases: dependence tests, scheduling and transitive closure approximation. It then points to unsolved problems and future work.



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