Modeling Consensus in a Process Calculus

Abstract

We give a process calculus model that formalizes a wellknown algorithm (introduced by Chandra and Toueg) solving consensus in the presence of a particular class of failure detectors (♦S); we use our model to formally prove that the algorithm satisfies its specification.

Unreliable Failure Detectors via Operational Semantics

“…Thus, in this paper, we provide a fresh look at the concept of failure detectors from the point of view of programming languages, using the formal tool of operational semantics. This paper complements previous work [NFM03] in which we used an operational semantics for a distributed process calculus to formally prove that a particular algorithm (also presented in [CT96]) solves the Distributed Consensus problem. Readers who are interested in proofs about algorithms within our new model (rather than proofs about it) are thus referred to our previous paper.…”

“…This theorem allows us to denote D(♦S/♦W)-runs as D(Ω)-runs, and justifies the model that we used when proving a Consensus algorithm correct in [NFM03]. We could prove Theorem 2 "directly" just like we did in the proof of Theorem 1.…”

“…An example of this can be found in our earlier paper [NFM03], where we used a reasonably standard process calculus to do this.…”

“…Usually, one considers only runs in which correct(F ) = ∅, i.e., in every run at least one process survives. Sometimes, as for the Consensus algorithm that we studied in [NFM03], it is even required that less than n/2 processes may crash. Abstractly, we use maxfail(n) to denote the maximal number of crashes permitted in a run.…”

On the Application of Formal Methods for Specifying and Verifying Distributed Protocols

“…Since their inception, they have been the subject of extensive research and they have been extended in various directions. Furthermore they have been used in the literature for reasoning about a variety of protocols (see, for example, [9,3,6,17] and [1,16,18] for I/O automata and PAs respectively).…”