Focus points and convergent process operators: a proof strategy for protocol verification

Abstract

We present a method for efficiently providing algebraic correctness proofs for communication systems. It is described in the setting of μCRL [J.F. Groote, A. Ponse, The syntax and semantics of μCRL, in: A. Ponse, C. Verhoef, S.F.M. van Vlijmen (Eds.), Algebra of Communicating Processes, Workshops in Computing, Springer, Berlin, 1994, pp. 26–62] which is, roughly, ACP [J.C.M. Baeten, W.P. Weijland, Process Algebra, Cambridge Tracts in Theoretical Computer Science, vol. 18, Cambridge University Press, Cambridge 1990, J.A. Bergstra, J.W. Klop, The algebra of recursively defined processes and the algebra of regular processes, in: Proceedings of the 11th ICALP, Antwerp, Lecture Notes in Computer Science, vol. 172, Springer, Berlin, 1984, pp. 82–95] extended with a formal treatment of the interaction between data and processes. The method incorporates assertional methods, such as invariants and simulations, in an algebraic framework, and centers around the idea that the state spaces of distributed systems are structured as a number of cones with focus points. As a result, it reduces a large part of algebraic protocol verification to the checking of a number of elementary facts concerning data parameters occurring in implementation and specification. The resulting method has been applied to various non-trivial case studies of which a number have been verified mechanically with the theorem checker PVS. In this paper the strategy is illustrated by several small examples and one larger example, the Concurrent Alternating Bit Protocol (CABP).