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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
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
On finite alphabets and infinite bases: From ready pairs to possible worlds
 In Proceedings 7th Conference on Foundations of Software Science and Computation Structures (FOSSACS’04), Barcelona, LNCS 2987
, 2004
"... Abstract. We prove that if a finite alphabet of actions contains at least two elements, then the equational theory for the process algebra BCCSP modulo any semantics no coarser than readiness equivalence and no finer than possible worlds equivalence does not have a finite basis. This semantic range ..."
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Cited by 9 (7 self)
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Abstract. We prove that if a finite alphabet of actions contains at least two elements, then the equational theory for the process algebra BCCSP modulo any semantics no coarser than readiness equivalence and no finer than possible worlds equivalence does not have a finite basis. This semantic range includes ready trace equivalence. 1
A finite basis for failure semantics
 In Proceedings 32nd Colloquium on Automata, Languages and Programming (ICALP’05), Lisbon, LNCS 3580
, 2005
"... Abstract. We present a finite ωcomplete axiomatization for the process algebra BCCSP modulo failure semantics, in case of a finite alphabet. This solves an open question by Groote [12]. 1 ..."
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Cited by 9 (7 self)
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Abstract. We present a finite ωcomplete axiomatization for the process algebra BCCSP modulo failure semantics, in case of a finite alphabet. This solves an open question by Groote [12]. 1
On finite alphabets and infinite bases III: Simulation
 Proc. CONCUR’06, LNCS 4137
, 2006
"... Abstract. This paper studies the (in)equational theory of simulation preorder and equivalence over the process algebra BCCSP. We prove that in the presence of a finite alphabet with at least two actions, the (in)equational theory of BCCSP modulo simulation preorder or equivalence does not have a fin ..."
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Cited by 5 (1 self)
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Abstract. This paper studies the (in)equational theory of simulation preorder and equivalence over the process algebra BCCSP. We prove that in the presence of a finite alphabet with at least two actions, the (in)equational theory of BCCSP modulo simulation preorder or equivalence does not have a finite basis. In contrast, in the presence of an alphabet that is infinite or a singleton, the equational theory for simulation equivalence does have a finite basis. 1
The Translation Power of the Futamura Projections
 In Perspectives of Systems Informatics, volume 2890 of LNCS
, 2003
"... Despite practical successes with the Futamura projections, it has been an open question whether target programs produced by specializing interpreters can always be as e#cient as those produced by a translator. We show that, given a Jonesoptimal program specializer with static expression reducti ..."
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Cited by 2 (0 self)
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Despite practical successes with the Futamura projections, it has been an open question whether target programs produced by specializing interpreters can always be as e#cient as those produced by a translator. We show that, given a Jonesoptimal program specializer with static expression reduction, there exists for every translator an interpreter which, when specialized, can produce target programs that are at least as fast as those produced by the translator. This is not the case if the specializer is not Jonesoptimal. We also examine Ershov's generating extensions, give a parameterized notion of Jones optimality, and show that there is a class of specializers that can always produce residual programs that match the size and time complexity of programs generated by an arbitrary generating extension. This is the class of generation universal specializers. We study these questions on an abstract level, independently of any particular specialization method.
On Finite Alphabets and Infinite Bases
"... Van Glabbeek (1990) presented the linear time – branching time spectrum of behavioral semantics. He studied these semantics in the setting of the basic process algebra BCCSP, and gave finite, sound and groundcomplete, axiomatizations for most of these semantics. Groote (1990) proved for some of van ..."
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Van Glabbeek (1990) presented the linear time – branching time spectrum of behavioral semantics. He studied these semantics in the setting of the basic process algebra BCCSP, and gave finite, sound and groundcomplete, axiomatizations for most of these semantics. Groote (1990) proved for some of van Glabbeek’s axiomatizations that they are ωcomplete, meaning that an equation can be derived if (and only if) all of its closed instantiations can be derived. In this paper we settle the remaining open questions for all the semantics in the linear time – branching time spectrum, either positively by giving a finite sound and groundcomplete axiomatization that is ωcomplete, or negatively by proving that such a finite basis for the equational theory does not exist. We prove that in case of a finite alphabet with at least two actions, failure semantics affords a finite basis, while for ready simulation, completed simulation, simulation, possible worlds, ready trace, failure trace and ready semantics, such a finite basis does not exist. Completed simulation semantics also lacks a finite basis in case of an infinite alphabet of actions.