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Complete and ready simulation semantics are not finitely based over BCCSP, even . . .
, 2011
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On the Existence of a Finite Base for Complete Trace Equivalence over BPA with Interrupt
, 2007
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On bisimilarity and substitution in presence of replication
 In 37th International Colloquium on Automata, Languages and Programming (ICALP), volume 6199 of LNCS
, 2010
"... Abstract. We prove a new congruence result for the picalculus: bisimilarity is a congruence in the subcalculus that does not include restriction nor sum, and features toplevel replications. Our proof relies on algebraic properties of replication, and on a new syntactic characterisation of bisi ..."
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Abstract. We prove a new congruence result for the picalculus: bisimilarity is a congruence in the subcalculus that does not include restriction nor sum, and features toplevel replications. Our proof relies on algebraic properties of replication, and on a new syntactic characterisation of bisimilarity. We obtain this characterisation using a rewriting system rather than a purely equational axiomatisation. We then deduce substitution closure, and hence, congruence. Whether bisimilarity is a congruence when replications are unrestricted remains open. 1
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
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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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.
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.
UNIFYING THE LINEAR TIMEBRANCHING TIME SPECTRUM OF STRONG PROCESS SEMANTICS
, 2012
"... Vol. 9(2:11)2013, pp. 1–74 www.lmcsonline.org ..."
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A GroundComplete Axiomatization of Stateless Bisimilarity over Linda ✩
"... This paper offers a finite, groundcomplete axiomatization of stateless bisimilarity over the tuplespacebased coordination language Linda. As stepping stones towards that result, axiomatizations of stateless bisimilarity over the sequential fragment of Linda without the nask primitive, and over th ..."
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This paper offers a finite, groundcomplete axiomatization of stateless bisimilarity over the tuplespacebased coordination language Linda. As stepping stones towards that result, axiomatizations of stateless bisimilarity over the sequential fragment of Linda without the nask primitive, and over the full sequential sublanguage are given. It is also shown that stateless bisimilarity coincides with standard bisimilarity over the sequential fragment of Linda without the nask primitive.
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.