Topic
Peterson's algorithm
About: Peterson's algorithm is a research topic. Over the lifetime, 30 publications have been published within this topic receiving 852 citations. The topic is also known as: Peterson's solution.
Papers
TL;DR: An algorithm is proposed that creates mutual exclusion in a computer network whose nodes communicate only by messages and do not share memory, and it is shown that the number can be contained in a fixed amount of memory by storing it as the residue of a modulus.
Abstract: An algorithm is proposed that creates mutual exclusion in a computer network whose nodes communicate only by messages and do not share memory. The algorithm sends only 2*(N - 1) messages, where N is the number of nodes in the network per critical section invocation. This number of messages is at a minimum if parallel, distributed, symmetric control is used; hence, the algorithm is optimal in this respect. The time needed to achieve mutual exclusion is also minimal under some general assumptions. As in Lamport's "bakery algorithm," unbounded sequence numbers are used to provide first-come firstserved priority into the critical section. It is shown that the number can be contained in a fixed amount of memory by storing it as the residue of a modulus. The number of messages required to implement the exclusion can be reduced by using sequential node-by-node processing, by using broadcast message techniques, or by sending information through timing channels. The "readers and writers" problem is solved by a simple modification of the algorithm and the modifications necessary to make the algorithm robust are described.
737 citations
TL;DR: A novel approach is proposed to reduce the LUT size by at least four times through making use of the properties of the error locator polynomial and normal basis representation of finite field elements.
Abstract: The forward error correction for 100-Gbit/s optical transport network has received much attention recently. Studies showed that product codes that employ three-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) codes can achieve better performance than other BCH or Reed-Solomon codes. For such codes, the Peterson algorithm can be used to compute the error locator polynomial, and its roots can be found directly using a lookup table (LUT). However, the size of the LUT is quite large for finite fields of high order. In this brief, a novel approach is proposed to reduce the LUT size by at least four times through making use of the properties of the error locator polynomial and normal basis representation of finite field elements. Moreover, hybrid representation of finite field elements is adopted to minimize the complexity of the involved computations. For a (1023, 993) BCH decoder over GF(210), the proposed design can lead to at least 28% complexity reduction.
37 citations
TL;DR: This work presents a “fine-grained” solution to the mutual exclusion problem and shows that the algorithm is correct even if shared variables are accessed nonatomically.
Abstract: We present a "fine-grained" solution to the mutual exclusion problem. A program isfine-grained if it uses only single-reader, single-writer boolean variables and if each of its atomic operations has at most one occurrence of at most one shared variable. In contrast to other fine-grained solutions that have appeared in the literature, processes in our solution do not bysy-wait, but wait on one another only by executingawait statements. Such statements can be implemented in practice either by means of context switching or by means of "local" spinning. We show that our algorithm is correct even if shared variables are accessed nonatomically.
21 citations
TL;DR: This work investigates some simple kinds of ITL formulas which have application to compositional reasoning and furthermore are closed under conjunction and the conventional temporal operator known both as “box” and “always”, and uses a natural form of time symmetry with 2-to-1 formulas.
Abstract: Interval Temporal Logic (ITL) is an established formalism for reasoning about time periods. We investigate some simple kinds of ITL formulas which have application to compositional reasoning and furthermore are closed under conjunction and the conventional temporal operator known both as "box" and "always". Such closures help us modularly construct formulas from simple building blocks in a way which preserves useful compositional properties. The most important class considered here is called the 2-to-1 formulas. They offer an attractive framework for analysing sequential composition in ITL and provide the formal basis for most of the subsequent presentation. A key contribution of this work concerns a useful and apparently new and quite elementary mathematical theorem that 2-to-1 formulas are closed under "box". We also use a natural form of time symmetry with 2-to-1 formulas. This extends known facts about such formulas by looking at them in reverse. An important example involves showing that 2-to-1 formulas are also closed under a variant of "box" for prefix subintervals rather than suffix ones. We then apply the compositional formulas obtained with time symmetry to analyse concurrent behaviour involving mutual exclusion in both Peterson's algorithm and a new and more abstract one. At present, our study of mutual exclusion mainly serves as a kind of experimental "proof of concept" and research tool to develop and illustrate some of the logical framework's promising features. We also discuss how time symmetry sometimes assists in reducing reasoning in ITL to conventional linear-time temporal logic.
16 citations
TL;DR: 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 is derived and a new n-process algorithm for mutual exclusion is presented that achieves the bound for any n.
Abstract: 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
10 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2019 | 2 |
| 2017 | 1 |
| 2016 | 2 |
| 2015 | 2 |
| 2014 | 3 |
| 2013 | 1 |