Layered reasoning for randomized distributed algorithms

Abstract

Abstract This paper adopts the communication closed layer (CCL) concept of Elrad and Francez to the formal reasoning of randomized distributed algorithms. We do so by enriching probabilistic automata (PA) with a layered composition operator, an intermediate between parallel and sequential composition. Layered composition is used to establish probabilistic counterparts of the CCL laws that exploit independence and/or precedence conditions between the constituent PA. The probabilistic CCL laws enable partial order (po-) equivalence when layered composition is replaced by sequential composition. Such po-equivalence induces a purely syntactic partial-order state space reduction via layered separation in compositions of PA while preserving probabilistic next-free linear-time properties. The feasibility of such layered separation is demonstrated on a randomized mutual exclusion algorithm by Kushilevitz and Rabin, complementing an algebraic approach (for analyzing this algorithm) by McIver, Gonzalia, Cohen, and Morgan.