Reduce the complexity of the polyhedron minimization using the max plus pruning method

Abstract

The polyhedral analysis is widely used for the static analysis of programs, thanks to its expressiveness but it is also time consuming. To deal with that, a sub-polyhedral analysis has been developed which offers a good tread off between expressiveness and sufficiency. This analysis is based on a set of directions which is defined statically at the beginning of the analysis. More the cardinality of Δ is big, more the precision of the result is high. Even if the set Δ is big, the sub-polyhedral analysis can be done in a linear time. The bottleneck is that to construct the resulting polyhedron with a large number of constraints (one constraints per direction) is time consuming. In this article, we present a minimization method that allows to deal with that, using the max plus pruning method. We demonstrate the efficiency of our method on some benchmarks. The first results are very encouraging.