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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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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
Complete and ready simulation semantics are not finitely based over BCCSP, even . . .
, 2011
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Axiomatizing Weak Ready Simulation Semantics over BCCSP
"... Ready simulation has proven to be one of the most significant semantics in process theory. It is at the heart of a number of general results that pave the way to a comprehensive understanding of the spectrum of process semantics. Since its original definition by Bloom, Istrail and Meyer in 1995, sev ..."
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Ready simulation has proven to be one of the most significant semantics in process theory. It is at the heart of a number of general results that pave the way to a comprehensive understanding of the spectrum of process semantics. Since its original definition by Bloom, Istrail and Meyer in 1995, several authors have proposed generalizations of ready simulation to deal with internal actions. However, a thorough study of the (non)existence of finite (in)equational bases for weak ready simulation semantics is still missing in the literature. This paper presents a complete account of positive and negative results on the axiomatizability of weak ready simulation semantics over the language BCCSP. In addition, this study offers a thorough analysis of the axiomatizability properties of weak simulation semantics.
The equational theory of weak complete simulation semantics over BCCSP
 SOFSEM 2012: Theory and Practice of Computer Science, 38th Conference on Current Trends in Theory and Practice of Computer Science
, 2012
"... Abstract. This paper presents a complete account of positive and negative results on the finite axiomatizability of weak complete simulation semantics over the language BCCSP. We offer finite (un)conditional groundcomplete axiomatizations for the weak complete simulation precongruence. In sharp cont ..."
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Abstract. This paper presents a complete account of positive and negative results on the finite axiomatizability of weak complete simulation semantics over the language BCCSP. We offer finite (un)conditional groundcomplete axiomatizations for the weak complete simulation precongruence. In sharp contrast to this positive result, we prove that, in the presence of at least one observable action, the (in)equational theory of the weak complete simulation precongruence over BCCSP does not have a finite (in)equational basis. In fact, the collection of (in)equations in at most one variable that hold in weak complete simulation semantics over BCCSP does not have an (in)equational basis of ‘bounded depth’, let alone a finite one. 1
On finite bases for weak semantics: Failures versus Impossible futures. Full version of current paper. Available at http:// arxiv.org/abs/0810.4904.
, 2008
"... Abstract. We provide a finite basis for the (in)equational theory of the process algebra BCCS modulo the weak failures preorder and equivalence. We also give positive and negative results regarding the axiomatizability of BCCS modulo weak impossible futures semantics. ..."
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Abstract. We provide a finite basis for the (in)equational theory of the process algebra BCCS modulo the weak failures preorder and equivalence. We also give positive and negative results regarding the axiomatizability of BCCS modulo weak impossible futures semantics.
Axiomatizing Weak Simulation Semantics over BCCSP
"... This paper is devoted to the study of the (in)equational theory of the largest (pre)congruences over the language BCCSP induced from internal steps in process behaviours. In particular, the article focuses on the (pre)congruences associated with the weak simulation, the weak complete simulation and ..."
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This paper is devoted to the study of the (in)equational theory of the largest (pre)congruences over the language BCCSP induced from internal steps in process behaviours. In particular, the article focuses on the (pre)congruences associated with the weak simulation, the weak complete simulation and the weak ready simulation preorders. For each of these behavioural semantics, results on the (non)existence of finite (ground)complete (in)equational axiomatizations are given. The axiomatization of those semantics using conditional equations is also discussed in some detail.
A Cancellation Theorem for BCCSP
"... This paper presents a cancellation theorem for the preorders in van Glabbeek’s linear timebranching time spectrum over BCCSP. Apart from having some intrinsic interest, the proven cancellation result plays a crucial role in the study of the cover equations, in the sense of Fokkink and Nain, that ..."
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This paper presents a cancellation theorem for the preorders in van Glabbeek’s linear timebranching time spectrum over BCCSP. Apart from having some intrinsic interest, the proven cancellation result plays a crucial role in the study of the cover equations, in the sense of Fokkink and Nain, that characterize the studied semantics. The techniques used in the proof of the cancellation theorem may also have some independent interest.
ON THE AXIOMATIZABILITY OF IMPOSSIBLE FUTURES
, 2015
"... Abstract. A general method is established to derive a groundcomplete axiomatization for a weak semantics from such an axiomatization for its concrete counterpart, in the context of the process algebra BCCS. This transformation moreover preserves ωcompleteness. It is applicable to semantics at lea ..."
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Abstract. A general method is established to derive a groundcomplete axiomatization for a weak semantics from such an axiomatization for its concrete counterpart, in the context of the process algebra BCCS. This transformation moreover preserves ωcompleteness. It is applicable to semantics at least as coarse as impossible futures semantics. As an application, groundand ωcomplete axiomatizations are derived for weak failures, completed trace and trace semantics. We then present a finite, sound, groundcomplete axiomatization for the concrete impossible futures preorder, which implies a finite, sound, groundcomplete axiomatization for the weak impossible futures preorder. In contrast, we prove that no finite, sound axiomatization for BCCS modulo concrete and weak impossible futures equivalence is groundcomplete. If the alphabet of actions is infinite, then the aforementioned groundcomplete axiomatizations are shown to be ωcomplete. If the alphabet is finite, we prove that the inequational theories of BCCS modulo the concrete and weak impossible futures preorder lack such a finite basis.