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A theory of communicating sequential processes
, 1984
"... A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account. ..."
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Cited by 4142 (17 self)
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A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account.
Algebraic laws for nondeterminism and concurrency
 Journal of the ACM
, 1985
"... Abstract. Since a nondeterministic and concurrent program may, in general, communicate repeatedly with its environment, its meaning cannot be presented naturally as an input/output function (as is often done in the denotational approach to semantics). In this paper, an alternative is put forth. Firs ..."
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Cited by 602 (13 self)
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Abstract. Since a nondeterministic and concurrent program may, in general, communicate repeatedly with its environment, its meaning cannot be presented naturally as an input/output function (as is often done in the denotational approach to semantics). In this paper, an alternative is put forth. First, a definition is given of what it is for two programs or program parts to be equivalent for all observers; then two program parts are said to be observation congruent iff they are, in all program contexts, equivalent. The behavior of a program part, that is, its meaning, is defined to be its observation congruence class. The paper demonstrates, for a sequence of simple languages expressing finite (terminating) behaviors, that in each case observation congruence can be axiomatized algebraically. Moreover, with the addition of recursion and another simple extension, the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties.
Process algebra for synchronous communication
 Inform. and Control
, 1984
"... Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite ..."
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Cited by 424 (66 self)
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Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite system behind the communication algebra is shown to be confluent and terminating (modulo its permutative reductions). Further, some relationships are shown to hold between the four concepts of merging. © 1984 Academic Press, Inc.
Branching Time and Abstraction in Bisimulation Semantics
 Journal of the ACM
, 1996
"... Abstract. In comparative concurrency semantics, one usually distinguishes between linear time and branching time semantic equivalences. Milner’s notion of ohsen~ation equirlalence is often mentioned as the standard example of a branching time equivalence. In this paper we investigate whether observa ..."
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Cited by 322 (17 self)
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Abstract. In comparative concurrency semantics, one usually distinguishes between linear time and branching time semantic equivalences. Milner’s notion of ohsen~ation equirlalence is often mentioned as the standard example of a branching time equivalence. In this paper we investigate whether observation equivalence really does respect the branching structure of processes, and find that in the presence of the unobservable action 7 of CCS this is not the case. Therefore, the notion of branching hisimulation equivalence is introduced which strongly preserves the branching structure of processes, in the sense that it preserves computations together with the potentials in all intermediate states that are passed through, even if silent moves are involved. On closed KSterms branching bisimulation congruence can be completely axiomatized by the single axiom scheme: a.(7.(y + z) + y) = a.(y + z) (where a ranges over all actions) and the usual laws for strong congruence. WC also establish that for sequential processes observation equivalence is not preserved under refinement of actions, whereas branching bisimulation is. For a large class of processes, it turns out that branching bisimulation and observation equivalence are the same. As far as we know, all protocols that have been verified in the setting of observation equivalence happen to fit in this class, and hence are also valid in the stronger setting of branching hisimulation equivalence.
Domain Theory in Logical Form
 Annals of Pure and Applied Logic
, 1991
"... The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and system ..."
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Cited by 253 (10 self)
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The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. • Logics of programs. Stone duality provides a junction between semantics (spaces of points = denotations of computational processes) and logics (lattices of properties of processes). Moreover, the underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e. properties which can be determined to hold of a process on the basis of a finite amount of information about its execution. These ideas lead to the following programme:
Structural Operational Semantics
 Handbook of Process Algebra
, 1999
"... Structural Operational Semantics (SOS) provides a framework to give an operational semantics to programming and specification languages, which, because of its intuitive appeal and flexibility, has found considerable application in the theory of concurrent processes. Even though SOS is widely use ..."
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Cited by 150 (19 self)
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Structural Operational Semantics (SOS) provides a framework to give an operational semantics to programming and specification languages, which, because of its intuitive appeal and flexibility, has found considerable application in the theory of concurrent processes. Even though SOS is widely used in programming language semantics at large, some of its most interesting theoretical developments have taken place within concurrency theory. In particular, SOS has been successfully applied as a formal tool to establish results that hold for whole classes of process description languages. The concept of rule format has played a major role in the development of this general theory of process description languages, and several such formats have been proposed in the research literature. This chapter presents an exposition of existing rule formats, and of the rich body of results that are guaranteed to hold for any process description language whose SOS is within one of these formats. As far as possible, the theory is developed for SOS with features like predicates and negative premises.
The Linear TimeBranching Time Spectrum I  The Semantics of Concrete, Sequential Processes
 Handbook of Process Algebra, chapter 1
"... this paper various semantics in the linear time  branching time spectrum are presented in a uniform, modelindependent way. Restricted to the class of finitely branching, concrete, sequential processes, only fifteen of them turn out to be different, and most semantics found in the literature that ..."
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Cited by 125 (4 self)
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this paper various semantics in the linear time  branching time spectrum are presented in a uniform, modelindependent way. Restricted to the class of finitely branching, concrete, sequential processes, only fifteen of them turn out to be different, and most semantics found in the literature that can be defined uniformly in terms of action relations coincide with one of these fifteen. Several testing scenarios, motivating these semantics, are presented, phrased in terms of `button pushing experiments' on generative and reactive machines. Finally twelve of these semantics are applied to a simple language for finite, concrete, sequential, nondeterministic processes, and for each of them a complete axiomatization is provided.
Turning SOS Rules into Equations
, 1994
"... Many process algebras are defined by structural operational semantics (SOS). Indeed, most such definitions are nicely structured and fit the GSOS format of [15]. We give a procedure for converting any GSOS language definition to a finite complete equational axiom system (possibly with one infinit ..."
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Cited by 97 (22 self)
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Many process algebras are defined by structural operational semantics (SOS). Indeed, most such definitions are nicely structured and fit the GSOS format of [15]. We give a procedure for converting any GSOS language definition to a finite complete equational axiom system (possibly with one infinitary induction principle) which precisely characterizes strong bisimulation of processes.
A brief history of process algebra
 Theor. Comput. Sci
, 2004
"... Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The a ..."
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Cited by 82 (1 self)
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Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.
Undecidable Problems in Unreliable Computations
 THEORETICAL COMPUTER SCIENCE
, 2000
"... Lossy counter machines are defined as Minsky ncounter machines where the values in the counters can spontaneously decrease at any time. While termination is decidable for lossy counter machines, structural termination (termination for every input) is undecidable. This undecidability result has f ..."
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Cited by 61 (3 self)
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Lossy counter machines are defined as Minsky ncounter machines where the values in the counters can spontaneously decrease at any time. While termination is decidable for lossy counter machines, structural termination (termination for every input) is undecidable. This undecidability result has far reaching consequences. Lossy counter machines can be used as a general tool to prove the undecidability of many problems, for example (1) The verification of systems that model communication through unreliable channels (e.g. model checking lossy fifochannel systems and lossy vector addition systems). (2) Several problems for reset Petri nets, like structural termination, boundedness and structural boundedness. (3) Parameterized problems like fairness of broadcast communication protocols.