13 research outputs found
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
CCS with Hennessy's merge has no finite-equational axiomatization
Abstract
This paper confirms a conjecture of Bergstra and Klop驴s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner驴s Calculus of Communicationg Systems is not finitely based modulo bisimulation equivalence. Thus Hennessy驴s merge cannot replace the left merge and communication merge operators proposed by Bergstra and Klop, at least if a finite axiomatization of parallel composition is desired.
2000 MATHEMATICS SUBJECT CLASSIFICATION: 08A70, 03B45, 03C05, 68Q10, 68Q45, 68Q55, 68Q70.
CR SUBJECT CLASSIFICATION (1991): D.3.1, F.1.1, F.1.2, F.3.2, F.3.4, F.4.1.
KEYWORDS AND PHRASES: Concurrency, process algebra, CCS, bisimulation, Hennessy驴s merge, left merge, communication merge, parallel composition, equational logic, complete axiomatizations, non-finitely based algebras
Nested Semantics over Finite Trees are Equationally Hard
This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based
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
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
An omega-complete Equational Specification of Interleaving
We consider the process theory PA that includes an operation for parallel composition, based on the interleaving paradigm. We prove that the standard set of axioms of PA is not !-complete by providing a set of axioms that are valid in PA, but not derivable from the standard ones. We prove that extending PA with this set yields an !-complete specification, which is finite in a setting with finitely many actions. 1991 Mathematics Subject Classification: 68Q10; 68Q65; 68Q70 1991 ACM Computing Classification System: D.1.3; F.1.1; F.1.2 Keywords and Phrases: Process Algebra, Algebraic Specification, Interleaving, !-completeness. Note: Research supported by the Netherlands Organization for Scientific Research (NWO) under contract SION 612-33-008. Work carried out under project SEN 2.1 Process Specification and Analysis. 1. Introduction The interleaving paradigm consists of the assumption that two atomic actions cannot happen at the same time, so that concurrency reduces to nondetermini..