20 research outputs found
On the Axiomatisation of Branching Bisimulation Congruence over CCS
In this paper we investigate the equational theory of (the restriction, relabelling, and recursion free fragment of) CCS modulo rooted branching bisimilarity, which is a classic, bisimulation-based notion of equivalence that abstracts from internal computational steps in process behaviour. Firstly, we show that CCS is not finitely based modulo the considered congruence. As a key step of independent interest in the proof of that negative result, we prove that each CCS process has a unique parallel decomposition into indecomposable processes modulo branching bisimilarity. As a second main contribution, we show that, when the set of actions is finite, rooted branching bisimilarity has a finite equational basis over CCS enriched with the left merge and communication merge operators from ACP
A Distribution Law for CCS and a New Congruence Result for the pi-calculus
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 pi-calculus in absence
of sum. To our knowledge, this is the only nontrivial subcalculus of the
pi-calculus that includes the full output prefix and for which strong
bisimilarity is a congruence.Comment: 20 page
Split-2 Bisimilarity has a Finite Axiomatization over CCS with<br> Hennessy's Merge
This note shows that split-2 bisimulation equivalence (also known as timed
equivalence) affords a finite equational axiomatization over the process
algebra obtained by adding an auxiliary operation proposed by Hennessy in 1981
to the recursion, relabelling and restriction free fragment of Milner's
Calculus of Communicating Systems. Thus the addition of a single binary
operation, viz. Hennessy's merge, is sufficient for the finite equational
axiomatization of parallel composition modulo this non-interleaving
equivalence. This result is in sharp contrast to a theorem previously obtained
by the same authors to the effect that the same language is not finitely based
modulo bisimulation equivalence
On the Axiomatisability of Parallel Composition
This paper studies the existence of finite equational axiomatisations of the
interleaving parallel composition operator modulo the behavioural equivalences
in van Glabbeek's linear time-branching time spectrum. In the setting of the
process algebra BCCSP over a finite set of actions, we provide finite,
ground-complete axiomatisations for various simulation and (decorated) trace
semantics. We also show that no congruence over BCCSP that includes
bisimilarity and is included in possible futures equivalence has a finite,
ground-complete axiomatisation; this negative result applies to all the nested
trace and nested simulation semantics
Unique Parallel Decomposition for the Pi-calculus
A (fragment of a) process algebra satisfies unique parallel decomposition if
the definable behaviours admit a unique decomposition into indecomposable
parallel components. In this paper we prove that finite processes of the
pi-calculus, i.e. processes that perform no infinite executions, satisfy this
property modulo strong bisimilarity and weak bisimilarity. Our results are
obtained by an application of a general technique for establishing unique
parallel decomposition using decomposition orders.Comment: In Proceedings EXPRESS/SOS 2016, arXiv:1608.0269
2-Nested Simulation is not Finitely Equationally Axiomatizable
2-nested simulation was introduced by Groote and Vaandrager [10] as the coarsest equivalence included in completed trace equivalence for which the tyft/tyxt format is a congruence format. In the lineartime-branching time spectrum of van Glabbeek [8], 2-nested simulationis one of the few equivalences for which no finite equational axiomatization is presented. In this paper we prove that such an axiomatizationdoes not exist for 2-nested simulation.Keywords: Concurrency, process algebra, basic CCS, 2-nested simulation, equational logic, complete axiomatizations