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42
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 89 (20 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.
Algebraic Theories for NamePassing Calculi
, 1996
"... In a theory of processes the names are atomic data items which can be exchanged and tested for identity. A wellknown example of a calculus for namepassing is the πcalculus, where names additionally are used as communication ports. We provide complete axiomatisations of late and early bisimulation ..."
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Cited by 41 (10 self)
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In a theory of processes the names are atomic data items which can be exchanged and tested for identity. A wellknown example of a calculus for namepassing is the πcalculus, where names additionally are used as communication ports. We provide complete axiomatisations of late and early bisimulation equivalences in such calculi. Since neither of the equivalences is a congruence we also axiomatise the corresponding largest congruences. We consider a few variations of the signature of the language; among these, a calculus of deterministic processes which is reminiscent of sequential functional programs with a conditional construct. Most of our axioms are shown to be independent. The axiom systems differ only by a few simple axioms and reveal the similarities and the symmetries of the calculi and the equivalences.
Refinement of Actions and Equivalence Notions for Concurrent Systems
 Acta Informatica
, 1998
"... This paper combines and extends the material of [GGa/c/d/e], except for the part in [GGc] on refinement of transitions in Petri nets and the discussion of TCSPlike parallel composition in [GGe]. An informal presentation of some basic ingredients of this paper appeared as [GGb]. Among others, th ..."
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Cited by 36 (1 self)
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This paper combines and extends the material of [GGa/c/d/e], except for the part in [GGc] on refinement of transitions in Petri nets and the discussion of TCSPlike parallel composition in [GGe]. An informal presentation of some basic ingredients of this paper appeared as [GGb]. Among others, the treatment of action refinement in stable and nonstable event structures is new. The research reported here was supported by Esprit project 432 (METEOR), Esprit Basic Research Action 3148 (DEMON), Sonderforschungsbereich 342 of the TU Munchen, ONR grant N0001492J1974 and the Human Capital and Mobility Cooperation Network EXPRESS (Expressiveness of Languages for Concurrency). Contents
Finite equational bases in process algebra: Results and open questions
 Processes, Terms and Cycles: Steps on the Road to Infinity, LNCS 3838
, 2005
"... Abstract. Van Glabbeek (1990) presented the linear time/branching time spectrum of behavioral equivalences for finitely branching, concrete, sequential processes. He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete axiomatizations for them. ..."
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Cited by 29 (19 self)
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Abstract. Van Glabbeek (1990) presented the linear time/branching time spectrum of behavioral equivalences for finitely branching, concrete, sequential processes. He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete axiomatizations for them. Obtaining such axiomatizations in concurrency theory often turns out to be difficult, even in the setting of simple languages like BCCSP. This has raised a host of open questions that have been the subject of intensive research in recent years. Most of these questions have been settled over BCCSP, either positively by giving a finite complete axiomatization, or negatively by proving that such an axiomatization does not exist. Still some open questions remain. This paper reports on these results, and on the stateoftheart in axiomatizations for richer process algebras with constructs like sequential and parallel composition. 1
Timing and Causality in Process Algebra
 Acta Informatica
, 1992
"... . There has been considerable controversy in concurrency theory between the `interleaving' and `true concurrency' schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences; the latter adopts more comple ..."
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Cited by 27 (0 self)
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. There has been considerable controversy in concurrency theory between the `interleaving' and `true concurrency' schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences; the latter adopts more complex semantic structures to avoid reducing concurrency to interleaving. In this paper we show that the two approaches are not irreconcilable. We define a timed process algebra where occurrences are associated with intervals of time, and give it a transition system semantics. This semantics has many of the advantages of the interleaving approach; the algebra admits an expansion theorem, and bisimulation semantics can be used as usual. Our transition systems, however, incorporate timing information, and this enables us to express concurrency: merely adding timing appropriately generalises transition systems to asynchronous transition systems, showing that time gives a link between true concurrenc...
CCS with Hennessy’s merge has no finite equational axiomatization
 Theoretical Computer Science
, 2005
"... This paper confirms a conjecture of Bergstra and Klop’s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner’s Calculus of Communicationg Systems is not finitely based modulo bisimulation equ ..."
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Cited by 20 (17 self)
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This paper confirms a conjecture of Bergstra and Klop’s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner’s Calculus of Communicationg Systems is not finitely based modulo bisimulation equivalence. Thus Hennessy’s merge cannot replace the left merge and communication merge operators proposed by Bergstra and Klop, at least if a finite axiomatization of parallel composition is desired.
Bisimulation is not Finitely (First Order) Equationally Axiomatisable
 in Proceedings 9 th Annual Symposium on Logic in Computer Science
, 1994
"... This paper considers the existence of finite equational axiomatisations of bisimulation over a calculus of finite state processes. To express even simple properties such as ¯XE = ¯XE[E=X] equationally it is necessary to use some notation for substitutions. Accordingly the calculus is embedded in a s ..."
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Cited by 17 (0 self)
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This paper considers the existence of finite equational axiomatisations of bisimulation over a calculus of finite state processes. To express even simple properties such as ¯XE = ¯XE[E=X] equationally it is necessary to use some notation for substitutions. Accordingly the calculus is embedded in a simply typed lambda calculus, allowing axioms such as the above to be written as equations of higher type rather than as equation schemes. Notions of higher order transition system and bisimulation are then defined and using them the nonexistence of finite axiomatisations containing at most first order variables is shown. The same technique is then applied to calculi of star expressions containing a zero process  in contrast to the positive result given in [FZ93] for BPA ? , which differs only in that it does not contain a zero. 1 Introduction In this paper we consider the existence of finite equational axiomatisations for bisimulation over finite state processes. Such questions of axio...
Synthesizing Distributed Transition Systems From Global Specifications
, 1999
"... We study the problem of synthesizing distributed implementations from global specifications. In particular, we characterize when a global transition system can be implemented as a synchronized product of local transition systems. Our work extends a number of previous studies in this area which h ..."
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Cited by 15 (0 self)
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We study the problem of synthesizing distributed implementations from global specifications. In particular, we characterize when a global transition system can be implemented as a synchronized product of local transition systems. Our work extends a number of previous studies in this area which have tended to make strong assumptions about the specificationeither in terms of determinacy or in terms of information concerning concurrency.
Ready to preorder: get your BCCSP axiomatization for free
 Proceedings of CALCO’07, volume 4624 of LNCS
, 2007
"... Abstract. This paper contributes to the study of the equational theory of the semantics in van Glabbeek’s linear time branching time spectrum over the language BCCSP, a basic process algebra for the description of finite synchronization trees. It offers an algorithm for producing a complete (respec ..."
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Cited by 14 (4 self)
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Abstract. This paper contributes to the study of the equational theory of the semantics in van Glabbeek’s linear time branching time spectrum over the language BCCSP, a basic process algebra for the description of finite synchronization trees. It offers an algorithm for producing a complete (respectively, groundcomplete) equational axiomatization of any behavioral congruence lying between ready simulation equivalence and partial traces equivalence from a complete (respectively, groundcomplete) inequational axiomatization of its underlying precongruence—that is, of the precongruence whose kernel is the equivalence. The algorithm preserves finiteness of the axiomatization when the set of actions is finite. 1
A finite equational base for CCS with left merge and communication merge
 Proceedings of ICALP’06 (part II), volume 4052 of Lecture Notes in Computer Science
, 2006
"... Abstract. Using the left merge and communication merge from ACP, we present an equational base (i.e., a groundcomplete and ωcomplete set of valid equations) for the fragment of CCS without recursion, restriction and relabelling. Our equational base is finite if the set of actions is finite. 1 ..."
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Cited by 10 (5 self)
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Abstract. Using the left merge and communication merge from ACP, we present an equational base (i.e., a groundcomplete and ωcomplete set of valid equations) for the fragment of CCS without recursion, restriction and relabelling. Our equational base is finite if the set of actions is finite. 1