Equational Verification of Cache Blocking in LU Decomposition using Kleene Algebra with Tests
Adam Barth, Dexter C. Kozen · 2002
In a recent paper of Mateev et al. (2001), a new technique for program analysis called fractal symbolic analysis was introduced and applied to verify the correctness of a series of source-level transformations for cache blocking in LU decomposition with partial pivoting. It was argued in that paper that traditional techniques are inadequate because the transformations break definition-use dependencies. We show how the task can be accomplished purely equationally using Kleene algebra with tests. 1