A Symbolic Approach to Bernstein Expansion for Program Analysis and Optimization

Several mathematical frameworks for static analysis of programs have been developed in the past decades. Although these tools are quite useful, they have still many limitations. In particular, integer multivariate polynomials arise in many situations while analyzing programs, and analysis systems are unable to handle such expressions. Although some dedicated methods have already been proposed, they only handle some subsets of such expressions. This paper presents an original and general approach to Bernstein expansion which is symbolic. Bernstein expansion allows bounding the range of a multivariate polynomial over a box and is generally more accurate than classic interval methods.