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Discrete Time Process Algebra with Silent Step
, 2000
"... The axiom system ACP of [10] was extended to discrete time in [6]. Here, we proceed to define the silent step in this theory in branching bisimulation semantics [7, 15] rather than weak bisimulation semantics [11, 20]. The version using relative timing is discussed extensively, versions using absolu ..."
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The axiom system ACP of [10] was extended to discrete time in [6]. Here, we proceed to define the silent step in this theory in branching bisimulation semantics [7, 15] rather than weak bisimulation semantics [11, 20]. The version using relative timing is discussed extensively, versions using absolute and parametric timing are presented in brief. A term model and a graph model are presented and soundness and completeness results are given. The time free theories BPA # and BPA # # are embedded in the discrete time theories. Examples of the use of the relative time theory are given by means of some calculations on communicating buffers. Note: Partial support received from ESPRIT Basic Research Action 7166, CONCUR2. This paper supersedes [4]. 1 Introduction Process algebra was introduced by Milner in the form of CCS [19]. The original design of CCS and of subsequent versions of process algebra such as ACP [10] and TCSP [14] involves no explicit notion of time. Time is present in the int...
Discrete Time Process Algebra and the Semantics of SDL
 CWI REPORT SENR9809, CENTRE FOR MATHEMATICS AND COMPUTER SCIENCE
, 1998
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DiscreteTime Process Algebra with Empty Process
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, 1997
"... We introduce an ACPstyle discretetime process algebra with relative timing, that features the empty process. Extensions to this algebra are described, and ample attention is paid to the considerations and problems that arise when introducing the empty process. We prove time determinacy, soundness, ..."
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Cited by 3 (3 self)
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We introduce an ACPstyle discretetime process algebra with relative timing, that features the empty process. Extensions to this algebra are described, and ample attention is paid to the considerations and problems that arise when introducing the empty process. We prove time determinacy, soundness, completeness, and the axioms of standard concurrency. 1991 Mathematics Subject Classification: 68Q10, 68Q22, 68Q55. 1991 CR Categories: D.1.3, D.3.1, F.1.2, F.3.2. Keywords: ACP, process algebra, discrete time, relative timing, empty process, time determinacy, soundness, completeness, axioms of standard concurrency, #,BPA  drt ID, BPA  drt,# ID, PA  drt,# ID, ACP  drt,# ID, BPA drt,# ID, PA drt,# ID, ACP drt,# ID, RSP(DEP). Note: The investigations of the second author were supported by the Netherlands Computer Science Research Foundation (SION) with financial support from the Netherlands Organization for Scientific Research (NWO). 3 Contents 1Introduction 5 1.1 Mo...
Fundamenta Informaticae 50(2002) 1–42 1 IOS Press Completeness of Timed CRL
"... Abstract. In [25] a straightforward extension of the process algebra £CRL was proposed to explicitly deal with time. The process algebra £CRL has been especially designed to deal with data in a process algebraic context. Using the features for data, only a minor extension of the language was needed ..."
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Abstract. In [25] a straightforward extension of the process algebra £CRL was proposed to explicitly deal with time. The process algebra £CRL has been especially designed to deal with data in a process algebraic context. Using the features for data, only a minor extension of the language was needed to obtain a very expressive variant of time. But [25] contains syntax, operational semantics and axioms characterising timed £CRL. It did not contain an in depth analysis of theory of timed £CRL. This paper fills this gap, by providing soundness and completeness results. The main tool to establish these is a mapping of timed to untimed £CRL and employing the completeness results obtained for untimed £CRL.
Discretetime Process Algebra and the Semantics of SDL
, 1997
"... We present an extension of discrete relative time process algebra where recursion, propositional signals, a counting process creation operator and the state operator are combined. A semantics of ' \Gamma SDL, a small subset of SDL that is closely connected with full SDL, is proposed which des ..."
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We present an extension of discrete relative time process algebra where recursion, propositional signals, a counting process creation operator and the state operator are combined. A semantics of ' \Gamma SDL, a small subset of SDL that is closely connected with full SDL, is proposed which describes the meaning of ' \Gamma SDL constructs using this extension of discrete relative time process algebra. This semantics allows for the generation of finitely branching transition systems for ' \Gamma SDL specifications. Jan Bergstra is a Professor of Programming and Software Engineering at the University of Amsterdam and a Professor of Applied Logic at Utrecht University, both in the Netherlands. His research interest is in mathematical aspects of software and system development, in particular in the design of algebras that can contribute to a better understanding of the relevant issues at a conceptual level. He is perhaps best known for his contributions to the field of process algeb...