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Book Chapter•DOI•

Concurrency and Automata on Infinite Sequences

David Park1•
University of Warwick1
23 Mar 1981-Theoretical Computer Science (Springer, Berlin, Heidelberg)-pp 167-183
TL;DR: A general method for proving/deciding equivalences between omega-regular languages, whose recognizers are modified forms of Buchi or Muller-McNaughton automata, derived from Milner's notion of “simulation” is obtained.
About: This article is published in Theoretical Computer Science.The article was published on 1981-03-23 and is currently open access. It has received 2256 citations till now. The article focuses on the topics: Abstract family of languages & Cone (formal languages).

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Summary

  • Park, D. M. R. (1981) Concurrency and automata on infinite sequences, also known as Original citation.
  • The version presented in WRAP is the published version or, version of record, and may be cited as it appears here.
  • The fixpoint identities can be used to elirninate iteration operators in favour' of various fixpoints.
  • Strictly, Lre are regarding subsets of I t {'Xr, Xrr..o.X,..,} as defining n-al:y finear functi.ons on extencied languages.
  • One of the steps here is notoriously hard.
  • So X is accessible iff X consists of accessible states, and is generated by some cycle, and iff X = In(n) for some infinite path n.

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Citations
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Book•
Principles of Model Checking

[...]

Christel Baier, Joost-Pieter Katoen
25 Apr 2008
TL;DR: Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.
Abstract: Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

4,905 citations

Cites background from "Concurrency and Automata on Infinit..."

  • ...bisimulation has been brought up independently by Milner [296] and Park [322]....

    [...]

Book•
Model Checking

[...]

Edmund M. Clarke1, Bernd-Holger Schlingloff2•
Carnegie Mellon University1, University of Bremen2
07 Jan 1999

4,478 citations

Book•
Distributed algorithms

[...]

Nancy Lynch
01 Jan 1996
TL;DR: This book familiarizes readers with important problems, algorithms, and impossibility results in the area, and teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures.
Abstract: In Distributed Algorithms, Nancy Lynch provides a blueprint for designing, implementing, and analyzing distributed algorithms. She directs her book at a wide audience, including students, programmers, system designers, and researchers. Distributed Algorithms contains the most significant algorithms and impossibility results in the area, all in a simple automata-theoretic setting. The algorithms are proved correct, and their complexity is analyzed according to precisely defined complexity measures. The problems covered include resource allocation, communication, consensus among distributed processes, data consistency, deadlock detection, leader election, global snapshots, and many others. The material is organized according to the system model-first by the timing model and then by the interprocess communication mechanism. The material on system models is isolated in separate chapters for easy reference. The presentation is completely rigorous, yet is intuitive enough for immediate comprehension. This book familiarizes readers with important problems, algorithms, and impossibility results in the area: readers can then recognize the problems when they arise in practice, apply the algorithms to solve them, and use the impossibility results to determine whether problems are unsolvable. The book also provides readers with the basic mathematical tools for designing new algorithms and proving new impossibility results. In addition, it teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures. Table of Contents 1 Introduction 2 Modelling I; Synchronous Network Model 3 Leader Election in a Synchronous Ring 4 Algorithms in General Synchronous Networks 5 Distributed Consensus with Link Failures 6 Distributed Consensus with Process Failures 7 More Consensus Problems 8 Modelling II: Asynchronous System Model 9 Modelling III: Asynchronous Shared Memory Model 10 Mutual Exclusion 11 Resource Allocation 12 Consensus 13 Atomic Objects 14 Modelling IV: Asynchronous Network Model 15 Basic Asynchronous Network Algorithms 16 Synchronizers 17 Shared Memory versus Networks 18 Logical Time 19 Global Snapshots and Stable Properties 20 Network Resource Allocation 21 Asynchronous Networks with Process Failures 22 Data Link Protocols 23 Partially Synchronous System Models 24 Mutual Exclusion with Partial Synchrony 25 Consensus with Partial Synchrony

4,340 citations

Journal Article•DOI•
Supervisory control of a class of discrete event processes

[...]

Peter J. Ramadge1, W. M. Wonham1•
University of Toronto1
01 Jan 1987-Siam Journal on Control and Optimization
TL;DR: In this paper, the control of a class of discrete event processes, i.e., processes that are discrete, asynchronous and possibly non-deterministic, is studied. And the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language, where the control process is described as the generator of a formal language, while the supervisor is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior.
Abstract: This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.

3,432 citations

Book•
Types and Programming Languages

[...]

Benjamin C. Pierce1•
University of Pennsylvania1
01 Jan 2002
TL;DR: This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages, with a variety of approaches to modeling the features of object-oriented languages.
Abstract: A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems -- and of programming languages from a type-theoretic perspective -- has important applications in software engineering, language design, high-performance compilers, and security.This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material.The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.

2,391 citations

Cites methods from "Concurrency and Automata on Infinit..."

  • ...The use of coinductive proof methods in computer science dates from the 1970s, for example in the work of Milner (1980) and Park (1981) on concurrency; also see Arbib and Manes’s categorical discussion of duality in automata theory (1975)....

    [...]

References
More filters
Journal Article•DOI•
Finite automata and their decision problems

[...]

Michael O. Rabin1, Dana Scott2•
Hebrew University of Jerusalem1, University of Chicago2
01 Apr 1959-Ibm Journal of Research and Development
TL;DR: Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.
Abstract: Finite automata are considered in this paper as instruments for classifying finite tapes. Each one-tape automaton defines a set of tapes, a two-tape automaton defines a set of pairs of tapes, et cetera. The structure of the defined sets is studied. Various generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined. Some decision problems concerning automata are shown to be solvable by effective algorithms; others turn out to be unsolvable by algorithms.

1,930 citations

Book Chapter•DOI•
Weak Second-Order Arithmetic and Finite Automata

[...]

J. Richakd Büchi
01 Jan 1960-Mathematical Logic Quarterly
TL;DR: The formalism of regular expressions was introduced by S. C. Kleene to obtain the following basic theorems.
Abstract: The formalism of regular expressions was introduced by S. C. Kleene [6] to obtain the following basic theorems.

1,132 citations

Journal Article•DOI•
Derivatives of Regular Expressions

[...]

Janusz A. Brzozowski1•
University of Ottawa1
01 Oct 1964-Journal of the ACM
TL;DR: In this paper the notion of a derivative of a regular expression is introduced atld the properties of derivatives are discussed and this leads, in a very natural way, to the construction of a state diagram from a regularexpression containing any number of logical operators.
Abstract: Kleene's regular expressions, which can be used for describing sequential circuits, were defined using three operators (union, concatenation and iterate) on sets of sequences. Word descriptions of problems can be more easily put in the regular expression language if the language is enriched by the inclusion of other logical operations. However, il~ the problem of converting the regular expression description to a state diagram, the existing methods either cannot handle expressions with additional operators, or are made quite complicated by the presence of such operators. In this paper the notion of a derivative of a regular expression is introduced atld the properties of derivatives are discussed. This leads, in a very natural way, to the construction of a state diagram from a regular expression containing any number of logical operators.

962 citations

Proceedings Article•
An algebraic definition of simulation between programs

[...]

Robin Milner1•
Stanford University1
01 Sep 1971
TL;DR: A technique is given and illustrated for proving simulation and equivalence of programs; there is an analogy with Floyd''s technique for proving correctness of programs.
Abstract: A simulation relation between programs is defined which is quasi-ordering. Mutual simulation is then an equivalence relation, and by dividing out by it we abstract from a program such details as how the sequencing is controlled and how data is represented. The equivalence classes are approxiamtions to the algorithms which are realized, or expressed, by their member programs. A technique is given and illustrated for proving simulation and equivalence of programs; there is an analogy with Floyd''s technique for proving correctness of programs. Finally, necessary and sufficient conditions for simulation are given.

616 citations

Journal Article•DOI•
Testing and generating infinite sequences by a finite automaton

[...]

Robert McNaughton1•
Massachusetts Institute of Technology1
01 Oct 1966-Information & Computation
TL;DR: Two apparently divergent areas of inquiry should give rise to the same problem, namely, that of describing the infinite history of finite automata, and it is this problem to which the remainder of this paper will address itself.
Abstract: Bfichi (1962) has given a decision procedure for a system of logic known as \" the Sequential Calculus,\" by showing that each well formed formula of the system is equivalent to a fornmla that, roughly speaking, says something about the infinite input history of a finite automaton. In so doing he managed to answer an open question that was of concern to pure logicians, some of whom had no interest in the theory of automata. Muller (1963) came upon quite similar concepts in studying a problem in asynchronous switching theory. The problem was to describe the behavior of an asynchronous circuit tha t does not reach any stability condition when starting from a certain state and subject to a certain input condition. Many different things can happen, since there is no control over how fast various parts of the circuit react with respect to each other. Since at no time during the presence of that input condition will the circuit reach a terminal condition, it will be possible to describe the total set of possibilities in an ideal fashioll only if an infinite amount of time is assumed for tha t input condition. Neither Biichi's Sequential Calculus nor ~Iuller's problem of asynchronous circuitry will be described further here. I t is interesting tha t two such apparently divergent areas of inquiry should give rise to the same problem, namely, that of describing the infinite history of finite automata. I t is this problem to which the remainder of this paper will address itself. I t will be recalled that a well known basic theorem in the theory of

553 citations

Related Papers (5)
Communication and Concurrency

[...]

01 Jan 1989
Robin Milner
A calculus of communicating systems

[...]

01 Jan 1980
Robin Milner
Algebraic laws for nondeterminism and concurrency

[...]

01 Jan 1985-Journal of the ACM
Matthew Hennessy, Robin Milner
Communicating Sequential Processes

[...]

01 Jan 1985
Tony Hoare
Testing equivalences for processes

[...]

01 Jan 1984-Theoretical Computer Science
R De Nicola, Matthew Hennessy
Frequently Asked Questions (1)
Q1. What are the contributions in this paper?

The paper is concerned with ways in which fair concurrency can be modeIled rr, sing notations for omega-: :egu-lar languages languages containing infinite seguences, whose recognizers a. re modified forms of Biichi or MuLler-McNaughton automata.