Verification of a Distributed Summation Algorithm

A correctness proof of a variant of Segall's Propagation of Information with Feedback protocol is outlined. The proof, which is carried out within the I/O automata model of Lynch and Tuttle, is standard except for the use of a prophecy variable. The aim of this paper is to show that, unlike what has been suggested in the literature, assertional methods based on invariant reasoning support an intuitive way to think about and understand this algorithm.

[1]  Martín Abadi,et al.  The existence of refinement mappings , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[2]  Nancy A. Lynch,et al.  Hierarchical correctness proofs for distributed algorithms , 1987, PODC '87.

[3]  Ching-Tsun Chou hchou Mechanical Veri cation of DistributedAlgorithms in Higher-Order Logic , 1993 .

[4]  Adrian Segall,et al.  Distributed network protocols , 1983, IEEE Trans. Inf. Theory.

[5]  Leslie Lamport,et al.  The temporal logic of actions , 1994, TOPL.

[6]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[7]  K. Mani Chandy Parallel program design , 1989 .

[8]  Frits W. Vaandrager,et al.  Proof-Checking a Data Link Protocol , 1994, TYPES.

[9]  Bengt Jonsson,et al.  Compositional specification and verification of distributed systems , 1994, TOPL.

[10]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[11]  Nancy A. Lynch,et al.  An introduction to input/output automata , 1989 .

[12]  A. Udaya Shankar,et al.  Protocol Verification via Projections , 1984, IEEE Transactions on Software Engineering.

[13]  F. Vaandrager Forward and Backward Simulations Part I : Untimed Systems , 1993 .

[14]  K. Mani Chandy,et al.  Parallel program design - a foundation , 1988 .

[15]  Ching-Tsun Chou Mechanical Verification of Distributed Algorithms in Higher-Order Logic , 1995, Comput. J..

[16]  Leslie Lamport,et al.  Specifying Concurrent Program Modules , 1983, TOPL.

[17]  Tobias Nipkow,et al.  I/Q Automata in Isabelle/HOL , 1994, TYPES.

[18]  Jan Friso Groote,et al.  Proof Theory for µCRL: A Language for Processes with Data , 1993, Semantics of Specification Languages.

[19]  Nancy A. Lynch,et al.  Computer-Assisted Simulation Proofs , 1993, CAV.