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21
On the axiomatizability of priority
 Proceedings of Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006
, 2006
"... Abstract. This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. It is proven that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, groundcomp ..."
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Cited by 15 (7 self)
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Abstract. This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. It is proven that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, groundcomplete equational axiomatization over that language. This negative result applies even if the syntax is extended with an arbitrary collection of auxiliary operators, and motivates the study of axiomatizations using conditional equations. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, groundcomplete axiomatization consisting of conditional equations over BCCSP. Sufficient conditions on the priority structure over actions are identified that lead to a finite, groundcomplete axiomatization of bisimulation equivalence using conditional equations. 1
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
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
On the Axiomatizability of Impossible Futures: Preorder versus Equivalence
, 2008
"... bisimulation We investigate the (in)equational theory of impossible futures semantics over the process algebra BCCSP. We prove that no finite, sound axiomatization for BCCSP modulo impossible futures equivalence is groundcomplete. By contrast, we present a finite, sound, groundcomplete axiomatizat ..."
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Cited by 5 (0 self)
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bisimulation We investigate the (in)equational theory of impossible futures semantics over the process algebra BCCSP. We prove that no finite, sound axiomatization for BCCSP modulo impossible futures equivalence is groundcomplete. By contrast, we present a finite, sound, groundcomplete axiomatization for BCCSP modulo impossible futures preorder. If the alphabet of actions is infinite, then this axiomatization is shown to be ωcomplete. If the alphabet is finite, we prove that the inequational theory of BCCSP modulo impossible futures preorder lacks such a finite basis. We also derive nonfinite axiomatizability results for nested impossible futures semantics. completed simulation simulation 2nested simulation ready simulation possible worlds ready traces failure traces readies failures completed traces possible futures impossible futures traces 1
A Distribution Law for CCS and a New Congruence Result for the Picalculus
 LMCS
"... Abstract. We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator. This axiomatisation is then used to derive congruence of strong bisimilarity in the finite πcalculus in absence of sum. To our knowledge, this is the only nontrivial subcalc ..."
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Cited by 4 (1 self)
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Abstract. We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator. This axiomatisation is then used to derive congruence of strong bisimilarity in the finite πcalculus in absence of sum. To our knowledge, this is the only nontrivial subcalculus of the πcalculus that includes the full output prefix and for which strong bisimilarity is a congruence.
The Saga of the Axiomatization of Parallel Composition ⋆
"... Abstract. This paper surveys some classic and recent results on the finite axiomatizability of bisimilarity over CCSlike languages. It focuses, in particular, on nonfinite axiomatizability results stemming from the semantic interplay between parallel composition and nondeterministic choice. The pa ..."
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Cited by 3 (0 self)
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Abstract. This paper surveys some classic and recent results on the finite axiomatizability of bisimilarity over CCSlike languages. It focuses, in particular, on nonfinite axiomatizability results stemming from the semantic interplay between parallel composition and nondeterministic choice. The paper also highlights the role that auxiliary operators, such as Bergstra and Klop’s left and communication merge and Hennessy’s merge operator, play in the search for a finite, equational axiomatization of parallel composition both for classic process algebras and for their realtime extensions. 1 The Problem and its History Process algebras are prototype description languages for reactive systems that arose from the pioneering work of figures like Bergstra, Hoare, Klop and Milner. Wellknown examples of such languages are ACP [18], CCS [44], CSP [40] and Meije [13]. These algebraic description languages for processes differ in the basic collection of operators that they offer for building new process descriptions from existing ones. However, since they are designed to allow for the description and analysis of systems of interacting processes, all these languages contain some form of parallel composition (also known as merge) operator allowing one to put two process terms in parallel with one another. These operators usually interleave the behaviours of their arguments, and support some form of synchronization between them. For example, Milner’s CCS offers the binary operator , whose intended semantics is described by the following classic rules in the style of Plotkin [49]. x µ → x ′ x   y µ → x ′   y y µ → y ′ x   y µ → x   y ′ x α → x ′ , y ¯α → y ′ x   y τ → x ′   y ′ (In the above rules, the symbol µ stands for an action that a process may perform, α and ¯α are two observable actions that may synchronize, and τ is a symbol denoting the result of their synchronization.)
Lifting NonFinite Axiomatizability Results to Extensions of Process Algebras
"... This paper presents a general technique for obtaining new results pertaining to the nonfinite axiomatizability of behavioural (pre)congruences over process algebras from old ones. The proposed technique is based on a variation on the classic idea of reduction mappings. In this setting, such reduct ..."
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Cited by 3 (1 self)
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This paper presents a general technique for obtaining new results pertaining to the nonfinite axiomatizability of behavioural (pre)congruences over process algebras from old ones. The proposed technique is based on a variation on the classic idea of reduction mappings. In this setting, such reductions are translations between languages that preserve sound (in)equations and (in)equational proofs over the source language, and reflect families of (in)equations responsible for the nonfinite axiomatizability of the target language. The proposed technique is applied to obtain a number of new nonfinite axiomatizability theorems in process algebra via reduction to Moller’s celebrated nonfinite axiomatizability result for CCS. The limitations of the reduction technique are also studied. In particular, it is shown that prebisimilarity is not finitely based over CCS with the divergent process Ω, but that this result cannot be proved by a reduction to the nonfinite axiomatizability of CCS modulo bisimilarity.
Rule Formats for Distributivity ⋆
"... Abstract. This paper proposes rule formats for Structural Operational Semantics guaranteeing that certain binary operators are left distributive with respect to a set of binary operators. Examples of leftdistributivity laws from the literature are shown to be instances of the provided formats. 1 ..."
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Cited by 2 (1 self)
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Abstract. This paper proposes rule formats for Structural Operational Semantics guaranteeing that certain binary operators are left distributive with respect to a set of binary operators. Examples of leftdistributivity laws from the literature are shown to be instances of the provided formats. 1
Is Observational Congruence on µExpressions Axiomatisable in Equational Horn Logic?
, 2007
"... It is well known that bisimulation on µexpressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features which go beyond pure equational Horn logic: either t ..."
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Cited by 1 (1 self)
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It is well known that bisimulation on µexpressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features which go beyond pure equational Horn logic: either the rules are impure by involving nonequational sideconditions, or they are schematically infinitary like the congruence rule which is not Horn. It is an open question whether these complications cannot be avoided in the prooftheoretically and computationally clean and powerful setting of secondorder equational Horn logic. This paper presents a positive and a negative result regarding axiomatisability of observational congruence in equational Horn logic. Firstly, we show how Milner’s impure rule system can be reworked into a pure Horn axiomatisation that is complete for guarded processes. Secondly, we prove that for unguarded processes, both Milner’s and Bloom/Ésik’s axiomatisations are incomplete without the congruence rule, and neither system has a complete extension in rank 1 equational axioms. It remains open whether there are higherrank equational axioms or Horn rules which would render Milner’s or Bloom / Ésik’s axiomatisations complete for unguarded processes.