Application of Symbolic Approach to the Bernstein Expansion for Program Analysis and Optimization

Mathematical packages for static analysis of programs have recently been developed. Although these packages are widely used, they have a number of limitations. In particular, they do not support multivariate polynomials with integer coefficients, which are often met in programs and used for the analysis of systems. Some methods to overcome this difficulty have already been suggested, but, unfortunately, they can be applied to only a subclass of such expressions. In this paper, we suggest a more general approach based on the Bernstein expansion, which facilitates the analysis of integer multivariate polynomials.