Section: New Results

Equivalence-Checking of Programs with Reductions

Participants : Guillaume Iooss, Christophe Alias, Sanjay Rajopadhye [Colorado State University, USA] .

Program equivalence is a well-known problem with a wide range of applications, such as algorithm recognition, program verification, and program optimization. This problem is also known to be undecidable if the class of programs is rich enough, in which case semi-algorithms are commonly used.

We focused on programs represented as systems of affine recurrence equations (SARE), defined over parametric polyhedral domains, a well-known formalism for the polyhedral model. SAREs include, as a proper subset, the class of affine control loop programs. Several semi-algorithms for program equivalence were already proposed for this class. Some take into account algebraic properties such as associativity and commutativity. To the best of our knowledge, none of them manage reductions, i.e., accumulations of a parametric number of sub-expressions using an associative and commutative operator. Our main contribution has been a new semi-algorithm to manage reductions. In particular, we outlined the ties between this problem and the perfect matching problem in a parametric bipartite graph.

This work was published at the SAS 2014 conference [7] .