Denotational semantics of concurrency

Bakker, J. W. de; Zucker, Jeffery I.

doi:10.1145/800070.802188

Cited by 51 publications

(41 citation statements)

References 18 publications

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“…This problem is overcome by defining two extra operators called left merge and communication merge, which both capture part of the behaviour of the merge. These operators were introduced by Bergstra and Klop [41], to answer an open question posed by de Bakker and Zucker [29].…”

Section: Left Merge and Communication Mergementioning

confidence: 99%

Introduction to Process Algebra

Fokkink

2000

Texts in Theoretical Computer Science. An EATCS Series

219

163

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Section: Left Merge and Communication Mergementioning

confidence: 99%

Introduction to Process Algebra

Fokkink

2000

Texts in Theoretical Computer Science. An EATCS Series

219

163

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“…(Examples: abc ~ abccb; abccb [3] = abc; abc [5] = abc; abc [O] is the empty word.) ( Proof (see, e.g., [6]).…”

Section: Definition (A)mentioning

confidence: 99%

“…is based on the theory of processes as sketched in [3] and described more fully in [ 4]. We briefly recall the main facts from this theory (in the terminology of [3,4] referring only to uniform processes).…”

Section: Bt Semantics: Mathematical Background and Semantic Equationsmentioning

confidence: 99%

“…Domain equations have been studied extensively by Scott [15,16] and, in a nondeterministic setting and using category theory, by Plotkin [14] and Smyth [17]. The theory of processes has been described elsewhere [3,4], and is included here to facilitate comparison between the LT and BT semantics (and to make the paper more self-contained). Section 2 is devoted to LT semantics, Section 3 to BT semantics, and Section 4 to the relationship between the two, and to some variations on the preceding definitions.…”

Section: Introductionmentioning

confidence: 99%

“…In order to do so, we need some preliminary facts which also have some independent interest. First we recall a definition from [3,4].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Linear time and branching time semantics for recursion with merge

Bakker¹,

Bergstra²,

Klop³

et al. 1983

Automata, Languages and Programming

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Abstract. We consider two ways of assigning semantics to a class of statements built from a set of atomic actions (the 'alphabet'), by means of sequential composition, nondeterministic choice, recursion and merge (arbitrary interleaving). The first is linear time semantics (LT), stated in terms of trace theory; the semantic domain is the collection of all closed sets of finite and infinite words. The second is branching time semantics (BT), as introduced by De Bakker and Zucker; here the semantic domain is the metric completion of the collection of finite processes. For LT we prove the continuity of the operations (merge, sequential composition) in a direct, combinatorial way.Next, a connection between LT and BT is established by means of the operation trace which assigns to a process its set of traces. We show that the trace set of a process is closed and that trace is continuous. This requires the compactness of the semantic domains, ensured by the finiteness of the alphabet. Using trace, we then can carry over BT into LT.

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Compactness in semantics for merge and fair merge

Bakker¹,

Zucker

1984

Logics of Programs

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An analysis of the role of compactness in defining the semantics of the merge and fair merge operations is provided. In a suitable context of hyperspaces (sets of subsets) a set is compact iff it is the limit of a sequence of finite sets; hence, compactness generalises bounded nondeterminaay. The merge operation is investigated in the setting of a simple language with elementary actions, sequential composition, nondeterministic choice and recursion. Metric topology is used as a framework to assign both a linear time and a branching time semantics to this language. It is then shown that the resulting meanings are compact trace sets and compact processes, respectively. This result complements previous work by De Bakker, Bergstra, Klop & Meyer. For the fair merge, an approach using scheduling through random choices is adopted -since a direct definition precludes the use of closed, let alone of compact sets. In the indirect approach, a compactness condition is used to show that the fair merge of two fair processes yields a fair process.

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Denotational semantics of concurrency

Cited by 51 publications

References 18 publications

Introduction to Process Algebra

Introduction to Process Algebra

Linear time and branching time semantics for recursion with merge

Compactness in semantics for merge and fair merge

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