A Lattice-structured Proof Technique Applied to a Minimum Spanning Tree Algorithm

Abstract

Higly-optimized concurrent algorithms are often hard to prove correct because they have no natural decomposition into separately provable parts. This paper presents a proof technique for the modular verification of such non-modular algorithms. It generalizes existing verification techniques based on a totally-ordered hierarchy of refinements to allow a partially-ordered hierarchy - that is, a lattice of different views of the algorithm. The technique is applied to the well-known distributed minimum spanning tree algorithm of Gallager, Humblet, and Spira, which has until recently lacked a rigorous proof.