A verification of the bakery protocol combining algebraic and model-oriented techniques

In this paper we give a specification of the so called Bakery protocol in an extension of the process algebra ACP with abstract datatypes. We prove that this protocol is equal to a Queue, modulo branching bisimulation equivalence. The verification is as follows. First we give a linear specification of the Bakery, that is a specification without parallelism. Then we introduce an invariant and encorporate this invariant into the linear specification of the Bakery and the specification of the Queue. Finally, we give a boolean function on the arguments of the resulting specification of the Bakery and the Queue, and we prove that by its equations it defines a branching bisimulation. This paper can be considered as an alternative to the proof of Groote and Korver [GK94], that proves the correctness of the Bakery protocol modulo weak bisimulation (or observational congruence) completely within the proof system of $mu$CRL