Using probabilistic Kleene algebra pKA for protocol verification

A.K. McIver, C. Gonzalia, E. Cohen, C.C. Morgan
2008 The Journal of Logic and Algebraic Programming  
We propose a method for verification of probabilistic distributed systems in which a variation of Kozen's Kleene Algebra with Tests [Dexter Kozen, Kleene algebra with tests, ACM Trans. Programming Lang. Syst. 19(3) (1997) 427-443] is used to take account of the well known interaction of probability and "adversarial" scheduling [Annabelle McIver, Carroll Morgan, Abstraction, Refinement and Proof for Probabilistic Systems, Technical Monographs in Computer Science, Springer-Verlag, New York,
more » ... We describe pKA, a probabilistic Kleene-style algebra, based on a widely accepted model of probabilistic/demonic computation [Jifeng He, K. Seidel, A.K. McIver, Probabilistic models for the guarded command language, Sci. Comput. Programming 28 (1997) 171-192; Roberto Segala, Modeling and verification of randomized distributed real-time systems, Separation theorems simplify reasoning about distributed systems, where with purely algebraic reasoning they can reduce complicated interleaving behaviour to "separated" behaviours each of which can be analysed on its own. Until now that has not been possible for probabilistic distributed systems. We present two case studies. The first treats a simple voting mechanism in the algebraic style, and the second-based on Rabin's Mutual exclusion with bounded waiting [Eyal Kushilevitz, M.O. Rabin, Randomized mutual exclusion algorithms revisited, in:
doi:10.1016/j.jlap.2007.10.005 fatcat:nuuhuzvb3bgrlcqykiw7opbw7a