Lamport's bakery algorithm

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.

Abstract: We introduce the (0, 1, ?)-counter abstraction method by which a parameterized system of unbounded size is abstracted into a finite-state system. Assuming that each process in the parameterized system is finite-state, the abstract variables are limited counters which count, for each local state s of a process, the number of processes which currently are in local state s. The counters are saturated at 2, which means that ?(s)= 2 whenever 2 or more processes are at state s. The emphasis of the paper is on the derivation of an adequate and sound set of fairness requirements (both weak and strong) that enable proofs of liveness properties of the abstract system, from which we can safely conclude a corresponding liveness property of the original parameterized system. We illustrate the method on few parameterized systems, including Szymanski's Algorithm for mutual exclusion. The method is also extended to deal with parameterized systems whose processes may have infinitely many local states, such as the Bakery Algorithm, by choosing few "interesting" state assertions and (0, 1, ?)-counting the number of processes satisfying them.

Abstract: We introduce the (0,1, oo)-counter abstraction method by which a parameterized system of unbounded size is abstracted into a finite-state system. Assuming that each process in the parameterized system is finite-state, the abstract variables are limited counters which count, for each local state s of a process, the number of processes which currently are in local state s. The counters are saturated at 2, which means that κ(s) = 2 whenever 2 or more processes are at state s. The emphasis of the paper is on the derivation of an adequate and sound set of fairness requirements (both weak and strong) that enable proofs of liveness properties of the abstract system, from which we can safely conclude a corresponding liveness property of the original parameterized system. We illustrate the method on few parameterized systems, including Szymanski's Algorithm for mutual exclusion. The method is also extended to deal with parameterized systems whose processes may have infinitely many local states, such as the Bakery Algorithm, by choosing few interesting state assertions and (0,1, ∞)-counting the number of processes satisfying them.

Abstract: This book is a celebration of Leslie Lamport's work on concurrency, interwoven in four-and-a-half decades of an evolving industry: from the introduction of the first personal computer to an era when parallel and distributed multiprocessors are abundant. His works lay formal foundations for concurrent computations executed by interconnected computers. Some of the algorithms have become standard engineering practice for fault tolerant distributed computing - distributed systems that continue to function correctly despite failures of individual components. He also developed a substantial body of work on the formal specification and verification of concurrent systems, and has contributed to the development of automated tools applying these methods. Part I consists of technical chapters of the book and a biography. The technical chapters of this book present a retrospective on Lamport's original ideas from experts in the field. Through this lens, it portrays their long-lasting impact. The chapters cover timeless notions Lamport introduced: the Bakery algorithm, atomic shared registers and sequential consistency; causality and logical time; Byzantine Agreement; state machine replication and Paxos; temporal logic of actions (TLA). The professional biography tells of Lamport's career, providing the context in which his work arose and broke new grounds, and discusses LaTeX - perhaps Lamport's most influential contribution outside the field of concurrency. This chapter gives a voice to the people behind the achievements, notably Lamport himself, and additionally the colleagues around him, who inspired, collaborated, and helped him drive worldwide impact. Part II consists of a selection of Leslie Lamport's most influential papers. This book touches on a lifetime of contributions by Leslie Lamport to the field of concurrency and on the extensive influence he had on people working in the field. It will be of value to historians of science, and to researchers and students who work in the area of concurrency and who are interested to read about the work of one of the most influential researchers in this field.