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Termination in Timed Process Algebra
 Formal Aspects of Computing
, 2000
"... We investigate different forms of termination in timed process algebras. The integrated framework of discrete and dense time, relative and absolute time process algebras is extended with forms of successful and unsuccessful termination. The different algebras are interrelated by embeddings and conse ..."
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Cited by 155 (25 self)
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We investigate different forms of termination in timed process algebras. The integrated framework of discrete and dense time, relative and absolute time process algebras is extended with forms of successful and unsuccessful termination. The different algebras are interrelated by embeddings and conservative extensions.
A Congruence Theorem for Structured Operational Semantics With Predicates
, 1993
"... . We proposed a syntactical format, the path format, for structured operational semantics in which predicates may occur. We proved that strong bisimulation is a congruence for all the operators that can be defined within the path format. To show that this format is useful we provided many examples t ..."
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Cited by 108 (5 self)
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. We proposed a syntactical format, the path format, for structured operational semantics in which predicates may occur. We proved that strong bisimulation is a congruence for all the operators that can be defined within the path format. To show that this format is useful we provided many examples that we took from the literature about CCS, CSP, and ACP; they do satisfy the path format but no formats proposed by others. The examples include concepts like termination, convergence, divergence, weak bisimulation, a zero object, side conditions, functions, real time, discrete time, sequencing, negative premises, negative conclusions, and priorities (or a combination of these notions). Key Words & Phrases: structured operational semantics, term deduction system, transition system specification, structured state system, labelled transition system, strong bisimulation, congruence theorem, predicate. 1980 Mathematics Subject Classification (1985 Revision): 68Q05, 68Q55. CR Categories: D.3.1...
A general conservative extension theorem in process algebra
 THEORETICAL COMPUTER SCIENCE
, 1994
"... We prove a general conservative extension theorem for transition system based process theories with easytocheck and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensur ..."
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Cited by 36 (4 self)
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We prove a general conservative extension theorem for transition system based process theories with easytocheck and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions
A Complete Equational Axiomatization for MPA with String Iteration
 DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, AALBORG UNIVERSITY
, 1995
"... We study equational axiomatizations of bisimulation equivalence for the language obtained by extending Milner's basic CCS with string iteration. String iteration is a variation on the original binary version of the Kleene star operation p*q obtained by restricting the first argument to be a ..."
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Cited by 13 (5 self)
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We study equational axiomatizations of bisimulation equivalence for the language obtained by extending Milner's basic CCS with string iteration. String iteration is a variation on the original binary version of the Kleene star operation p*q obtained by restricting the first argument to be a nonempty sequence of atomic actions. We show that, for every positive integer k, bisimulation equivalence over the set of processes in this language with loops of length at most k is finitely axiomatizable. We also offer a countably infinite equational theory that completely axiomatizes bisimulation equivalence over the whole language. We prove that this result cannot be improved upon by showing that no finite equational axiomatization of bisimulation equivalence over basic CCS with string iteration can exist, unless the set of actions is empty.
Process Algebra with Recursive Operations
"... ing from just the two atomic actions in I def = fthrow; tailg, FIR b 1 yields I ((throw tail) throw head) = head: First, observe I (throw tail) = . Then, using (4), it easily follows that I ((throw tail) throw head) = head: This expresses that head eventually comes up, and thus ex ..."
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Cited by 10 (5 self)
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ing from just the two atomic actions in I def = fthrow; tailg, FIR b 1 yields I ((throw tail) throw head) = head: First, observe I (throw tail) = . Then, using (4), it easily follows that I ((throw tail) throw head) = head: This expresses that head eventually comes up, and thus excludes the infinite sequence of steps present in I ((throw tail) throw head). 7.2 Empty Process Let the symbol " denote the empty process, introduced as a unit for sequential composition by Koymans and Vrancken in [58] (see also [28, 74]). Obvious as " may be (being a unit for \Delta), its introduction is nontrivial because at the same time it must be a unit for k as well. In the design of BPA, PA, ACP and related axiom systems, it has proved useful to study versions of the theory, both with and without ". Just for this reason the star operation with its (original) defining equation as given by Kleene in [54] was introduced in process algebra. Taking y = " in x y, one obtains x ...
Reniers. Timed process algebra (with a focus on explicit termination and relativetiming
 Proceedings of the International School on Formal Methods for the Design of RealTime Systems (SFMRT’04), volume 3185 of Lecture Notes in Computer Science
, 2004
"... Abstract. We treat theory and application of timed process algebra. We focus on a variant that uses explicit termination and action prefixing. This variant has some advantages over other variants. We concentrate on relative timing, but the treatment of absolute timing is similar. We treat both discr ..."
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Cited by 5 (2 self)
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Abstract. We treat theory and application of timed process algebra. We focus on a variant that uses explicit termination and action prefixing. This variant has some advantages over other variants. We concentrate on relative timing, but the treatment of absolute timing is similar. We treat both discrete and dense timing. We build up the theory incrementally. The different algebras are interrelated by embeddings and conservative extensions. As an example, we consider the PAR communication protocol. 1
Timing the untimed: Terminating successfully while being conservative
 In Middeldorp et al
, 2005
"... Abstract. There have been several timed extensions of ACPstyle process algebras with successful termination. None of them, to our knowledge, are equationally conservative (ground)extensions of ACP with successful termination. Here, we point out some design decisions which were the possible causes ..."
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Cited by 4 (1 self)
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Abstract. There have been several timed extensions of ACPstyle process algebras with successful termination. None of them, to our knowledge, are equationally conservative (ground)extensions of ACP with successful termination. Here, we point out some design decisions which were the possible causes of this misfortune and by taking different decisions, we propose a spectrum of timed process algebras ordered by equational conservativity ordering. 1 The Untimed Past The term “process algebra ” was coined by Jan Bergstra and Jan Willem Klop in [9] to denote an algebraic approach to concurrency theory. Their process algebra had uniform atomic actions ai for i ∈ I (with I some index set), sequential composition · , choice (alternative composition) + and leftmerge � as the basic composition operators. 1 Much of the core theory of [9] remained intact in the course of more than 20 years of developments in the ACPschool (for Algebra of Communicating
DiscreteTime Process Algebra with Empty Process
 Dat is dus heel interessant
, 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...
A Process Calculus with Finitary Comprehended Terms
, 903
"... Abstract. Meadow enriched ACP process algebras are essentially enrichments of models of the axiom system ACP that concern processes in which data are involved, the mathematical structure of data being a meadow. For all associative operators from the signature of meadow enriched ACP process algebras, ..."
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Abstract. Meadow enriched ACP process algebras are essentially enrichments of models of the axiom system ACP that concern processes in which data are involved, the mathematical structure of data being a meadow. For all associative operators from the signature of meadow enriched ACP process algebras, we introduce variablebinding operators as generalizations. These variablebinding operators, which give rise to comprehended terms, have the property that they can always be eliminated. Thus, we obtain a process calculus whose terms can be interpreted in all meadow enriched ACP process algebras. Use of the variablebinding operators that bind variables with a twovalued range can already have a major impact on the size of terms.
A Complete Equational Axiomatization for BPAdeltaɛ with Prefix Iteration
"... Prefix iteration x is added to Basic Process Algebra with deadlock and empty process. We present a finite equational axiomatization for this process algebra, and we prove that this axiomatization is complete with respect to strong bisimulation equivalence. This result is a mild generalization of a s ..."
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Prefix iteration x is added to Basic Process Algebra with deadlock and empty process. We present a finite equational axiomatization for this process algebra, and we prove that this axiomatization is complete with respect to strong bisimulation equivalence. This result is a mild generalization of a similar result in the setting of basic CCS in Fokkink (1994b). To obtain this completeness result, we set up a rewrite system, based on the axioms. In order to prove that this rewrite system is terminating modulo AC of the +, we generalize a termination theorem from Zantema and Geser (1994) to the setting of rewriting modulo equations. Finally, we show that bisimilar normal forms are syntactically equal modulo AC of the +.