The assertional versus Tarskian methods

In this lecture we analyze Peterson’s well known two-process criticalsection protocol [3] and prove that the mutual exclusion property holds. Our main aim is to explain two approaches by which the correctness of this protocol can be established. The first is the assertional method of proof which is the standard approach to concurrency. This approach uses the notions of global states, steps and histories. The second approach is event-based rather than state-based, and the notion of Tarskian system execution is used in the formalizing of an event-based proof. 1 Mutual exclusion protocol A critical section is a part of a program that must be executed in isolation from any other process critical-section execution. The critical section problem is to devise a protocol that prevents simultaneous access by two or more processes into their critical sections. For example, a process that sends a file to a printer needs to know that no other process can access the printer during the time of printing. Protocols that guarantee this separation are said to have the mutual exclusion property. An additional property is clearly required: that any process requesting its critical section will be able to access it sooner or later. This desirable “liveness” property is called the lockout freedom property. We will prove here the mutual exclusion property and leave the liveness properties as an exercise. Before we present Peterson’s algorithm in details, we want to discuss mutual exclusion algorithms in general. We follow Lamport’s fundamental paper [2]. ∗Departments of Mathematics and Computer Science, Ben-Gurion University. Models for Concurrency 2014.