Results 1 
6 of
6
Finite equational bases in process algebra: Results and open questions
 Processes, Terms and Cycles: Steps on the Road to Infinity, LNCS 3838
, 2005
"... Abstract. Van Glabbeek (1990) presented the linear time/branching time spectrum of behavioral equivalences for finitely branching, concrete, sequential processes. He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete axiomatizations for them. ..."
Abstract

Cited by 30 (21 self)
 Add to MetaCart
(Show Context)
Abstract. Van Glabbeek (1990) presented the linear time/branching time spectrum of behavioral equivalences for finitely branching, concrete, sequential processes. He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete axiomatizations for them. Obtaining such axiomatizations in concurrency theory often turns out to be difficult, even in the setting of simple languages like BCCSP. This has raised a host of open questions that have been the subject of intensive research in recent years. Most of these questions have been settled over BCCSP, either positively by giving a finite complete axiomatization, or negatively by proving that such an axiomatization does not exist. Still some open questions remain. This paper reports on these results, and on the stateoftheart in axiomatizations for richer process algebras with constructs like sequential and parallel composition. 1
CCS with Hennessy’s merge has no finite equational axiomatization
 Theoretical Computer Science
, 2005
"... This paper confirms a conjecture of Bergstra and Klop’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’s Calculus of Communicationg Systems is not finitely based modulo bisimulation equ ..."
Abstract

Cited by 20 (17 self)
 Add to MetaCart
(Show Context)
This paper confirms a conjecture of Bergstra and Klop’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’s Calculus of Communicationg Systems is not finitely based modulo bisimulation equivalence. Thus Hennessy’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.
Infinite SeriesParallel Posets: Logic and Languages
, 2000
"... We show that a set of uniformly widthbounded infinite seriesparallel pomsets is !seriesrational iff it is axiomatizable in monadic second order logic iff it is !recognizable. This extends recent work by Lodaya and Weil on sets of finite seriesparallel pomsets in two aspects: It relates their n ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
We show that a set of uniformly widthbounded infinite seriesparallel pomsets is !seriesrational iff it is axiomatizable in monadic second order logic iff it is !recognizable. This extends recent work by Lodaya and Weil on sets of finite seriesparallel pomsets in two aspects: It relates their notion of seriesrationality to logical concepts, and it generalizes the equivalence of recognizability and seriesrationality to infinite seriesparallel pomsets.
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 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
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.)
The Quest for Equational Axiomatizations of Parallel Composition: Status and Open Problems
, 2005
"... ..."
(Show Context)
Composition ⋆
, 909
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
Abstract
 Add to MetaCart
(Show Context)
Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS