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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 45 (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
Termination, deadlock, and divergence
 Journal of the ACM
"... Abstract. In this paper, a process algebra that incorporates expliclt representations of successful termination, deadlock, and divergence is introduced and its semantic theory is analyzed. Both an operational and a denotational semantics for the language is given and it is shown that they agree. The ..."
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Cited by 40 (14 self)
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Abstract. In this paper, a process algebra that incorporates expliclt representations of successful termination, deadlock, and divergence is introduced and its semantic theory is analyzed. Both an operational and a denotational semantics for the language is given and it is shown that they agree. The operational theory N based upon a suitable adaptation of the notion of bisimulation preorder. The denotational semantics forthelanguage isgiven interms of theinitial continuous algebra that satisfiesa set of equations E, CI~. It is shown that C’IE is fully abstract with respect to our choice of behavioral preorder. Several results ofindependent interest are obtained; namely, the finite approximability of the behavioral preorder and a partial completeness result for the set of equations E with respect to the preorder.
The importance of the left merge operator in process algebras
 Proceedings 17 th ICALP
"... Abstract. In this paper, we examine quational a~xiomatisations for PA, the process algebra of Bergstra and Klop, which is a simple subset of their full language ACP. The language PA has two combinators for concurrent execution: theusual full merge operator ~ and the more esoteric left merge operator ..."
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Cited by 32 (0 self)
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Abstract. In this paper, we examine quational a~xiomatisations for PA, the process algebra of Bergstra and Klop, which is a simple subset of their full language ACP. The language PA has two combinators for concurrent execution: theusual full merge operator ~ and the more esoteric left merge operator [. Though this latter combinator is somewhat semantically unusual, we demonstrate its importance by proving that, whereas a finite sound and complete equa ional theory exists for PA, no such finite theory can exist for PA in the absence of the left merge operator. 1
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 (20 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 m ..."
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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 19 (16 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.
Split and ST bisimulation semantics
 Information and Computation
"... In this paper the notion of action atomicity is relaxed by permitting actions to be observed in the middle of their evolution. Non atomic semantic equivalences, based on the notion of bisimulation, are studied over stable event structures. Splitn bisimulation equivalence (denoted n ¸) considers ea ..."
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Cited by 12 (3 self)
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In this paper the notion of action atomicity is relaxed by permitting actions to be observed in the middle of their evolution. Non atomic semantic equivalences, based on the notion of bisimulation, are studied over stable event structures. Splitn bisimulation equivalence (denoted n ¸) considers each event as composed of n phases. ST bisimulation equivalence (denoted ST ¸ ) is a slight refinement of 2 ¸ where each ending phase is unambiguously associated to a beginning phase. We prove that, by increasing n, we get finer and finer equivalences (i.e. n+1 ¸ ` n ¸) and, moreover, that n+1 ¸ coincides with ST ¸ over those event structures whose autoconcurrency is at most n. The main consequence of these results is that, for image finite event structures, ST ¸ is the intersection of all the n ¸. 1 Introduction Most of the behavioural equivalences for concurrent systems are usually based on the assumption that the execution of an action is an atomic activity which cannot b...
Some of My Favourite Results in Classic Process Algebra
 In Bulletin of the EATCS
, 2003
"... this paper has generated a veritable industry of results on the metatheory of SOS and process algebras. (See [10] for a mention of some of these achievements and pointers to the original literature.) The proof techniques used in these results were extremely ingenious, and have paved the way to many ..."
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Cited by 9 (4 self)
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this paper has generated a veritable industry of results on the metatheory of SOS and process algebras. (See [10] for a mention of some of these achievements and pointers to the original literature.) The proof techniques used in these results were extremely ingenious, and have paved the way to many similar developments. Again, the role played by the modal characterizations of behavioural equivalences in the proof of the characterizations of the largest congruences is remarkable
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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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