Peterson's Mutual Exclusion Algorithm Research Articles

Analysing Mutual Exclusion using Process Algebra with Signals

In contrast to common belief, the Calculus of Communicating Systems (CCS) and similar process algebras lack the expressive power to accurately capture mutual exclusion protocols without enriching the language with fairness assumptions. Adding a fairness assumption to implement a mutual exclusion protocol seems counter-intuitive. We employ a signalling operator, which can be combined with CCS, or other process calculi, and show that this minimal extension is expressive enough to model mutual exclusion: we confirm the correctness of Peterson's mutual exclusion algorithm for two processes, as well as Lamport's bakery algorithm, under reasonable assumptions on the underlying memory model. The correctness of Peterson's algorithm for more than two processes requires stronger, less realistic assumptions on the underlying memory model.

Modelling Peterson Mutual Exclusion Algorithm in DVE Language and Verifying LTL Properties

Peterson mutual exclusion algorithm is a concurrent programming algorithm for mutual exclusion that allows two processes to share a single-use resource without conflict, using only shared memory for communication. DiVinE is a LTL model checker, and DVE is the specification language. In this paper, we implement the DVE model of Peterson mutual exclusion algorithm, and verify LTL properties of Peterson mutual exclusion algorithms using DiVinE model checker. The experimental results show that the LTL formula structure is relevant to the costs of LTL verification.

Rewriting Semantics and Analysis of Concurrency Features for a C-like Language

This paper shows how one can easily transform K definitions of programming languages into runtime verification tools. To increase the confidence that these runtime verification tools can be used for testing real-world programs, the paper uses KernelC, a subset of the C programming language containing functions, memory allocation, pointer arithmetic, and input/output, which can be used to execute and test real C programs. KernelC is extended with threads and synchronization constructs, and two concurrent semantics are derived from its sequential semantics. The first semantics, defining a sequentially consistent memory model, can be easily transformed into a runtime verification tool for checking datarace and deadlock freeness. The second semantics defines in a relatively minimal fashion a relaxed memory model based on the x86-TSO memory model. By exploring the executions of an implementation of Peterson's mutual exclusion algorithm for both definitions, it is shown that the algorithm guarantees mutual exclusion for the sequentially consistent model, but cannot guarantee it for the relaxed model, but also that by allowing fence operations in the language, the algorithm can be fixed and proven correct for the TSO model, too.

Tight Bounds for Critical Sections in Processor Consistent Platforms

Most weak memory consistency models are incapable of supporting a solution to mutual exclusion using only read and write operations to shared variables. Processor consistency-Goodman's version (PC-G) is an exception. Ahamad et al. showed that Peterson's mutual exclusion algorithm is correct for PC-G, but Lamport's bakery algorithm is not. This paper derives a lower bound on the number of and type of (single or multiwriter) variables that a mutual exclusion algorithm must use in order to be correct for PC-G. Specifically, any such solution for n processes must use at least one multiwriter variable and n single-writer variables. Peterson's algorithm for two processes uses one multiwriter and two single-writer variables, and therefore establishes that this bound is tight for two processes. This paper presents a new n-process algorithm for mutual exclusion that is correct for PC-G and achieves the bound for any n. While Peterson's algorithm is fair, this extension to arbitrary n is not fair. Six known algorithms that use the same number and type of variables are shown to fail to guarantee mutual exclusion when the memory consistency model is only PC-G, as opposed to the sequential consistency model for which they were designed. A corollary of our investigation is that, in contrast to sequential consistency, multiwriter variables cannot be implemented from single-writer variables in a PC-G system

A mutual exclusion algorithm with optimally bounded bypasses

Peterson's algorithm [G.L. Peterson, Myths about the mutual exclusion problem, Inform. Process. Lett. 12 (3) (1981) 115–116] for mutual exclusion has been widely studied for its elegance and simplicity. In Peterson's algorithm, each process has to cross n − 1 stages to access the shared resource irrespective of the contention for the shared resource at that time, and allows unbounded bypasses. In [K. Block, T.-K. Woo, A more efficient generalization of Peterson's mutual exclusion algorithm, Inform. Process. Lett. 35 (1990) 219–222], Block and Woo proposed a modified algorithm that transforms the number stages to be crossed from fixed n − 1 to t, where 1 ⩽ t ⩽ n , and bounds the number of possible bypasses by n ( n − 1 ) / 2 . This paper proposes a simple modification that reduces the bound on the number of possible bypasses to optimal n − 1 .

Peterson's mutual exclusion algorithm revisited

A new derivation of Peterson's well-known mutual exclusion algorithm is presented. The derivation is driven by the formally stated requirements of Individual Progress, as opposed to the more traditional approach which starts from the requirement of Mutual Exclusion. The only formalisms used in the derivation are the predicate calculus and the theory of Owicki and Gries. No use is made of temporal logic. In particular, the so complicating oscillating behaviour of an await-condition is fully absorbed by the use of a variant function.

A more efficient generalization of Peterson's mutual exclusion algorithm

The algorithm presented depends on the number of processes interested in the critical section rather than n. If a process is at a level greater than or equal to the number of processes interested then it is a level higher than any other process and is permitted to enter the critical section.