Classification with Tarskian system executions (Bakery Algorithms as an example)

We argue that predicate languages and their Tarskian structures have an important place for the study of concurrency. The argument in our paper is based on an example: we show that two seemingly dissimilar algorithms have a common set of high-level properties, which reveals their affinity. The algorithms are a variant of Lamport's Bakery Algorithm and the Ricart and Agrawala algorithm. They seem different because one uses shared memory and the other message passing for communication. Yet it is intuitively obvious that they are in some sense very similar, and they belong to the same "family of Bakery Algorithms". The aim of this paper is to express in a formal way this intuition that classifies the two algorithms together. For this aim of expressing the abstract high level properties that are shared by the two algorithms we use predicate languages and their Taskian structures. We find a set of properties expressed in quantification language which are satisfied by every Tarskian system execution that models a run by either one of the protocols, and which is strong enough to ensure that the mutual exclusion property holds in these runs.