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A Distribution Law for CCS and a New Congruence Result for the π-calculus

Daniel Hirschkoff, Damien Pous, Helmut Seidl
2008 Logical Methods in Computer Science  
This axiomatisation is then used to derive congruence of strong bisimilarity in the finite pi-calculus in absence of sum.  ...  We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator.  ...  We are grateful to Arnaud Carayol for interesting discussions at early stages of this work, and to Ilaria Castellani for discussions about distributed bisimilarity.  ... 
doi:10.2168/lmcs-4(2:4)2008 fatcat:tguh6fs5wfddvaufltn4x74qyu

On the Axiomatisability of Parallel Composition: A Journey in the Spectrum

Luca Aceto, Valentina Castiglioni, Anna Ingólfsdóttir, Bas Luttik, Mathias Ruggaard Pedersen, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
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.  ...  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  ...  Acknowledgements We thank the anonymous reviewers for their valuable comments, and Rob van Glabbeek for a fruitful discussion on the axiomatisability of failures equivalence.  ... 
doi:10.4230/lipics.concur.2020.18 dblp:conf/concur/AcetoCILP20 fatcat:oh4zqxm3mneodc46rapj44y5l4

Nonaxiomatisability of equivalences over finite state processes

Peter Sewell
1997 Annals of Pure and Applied Logic  
This paper considers the existence of finite equational axiomatisations of behavioural equivalences over a calculus of finite state pTOCCSSeS. To express even simple properties such as pxE = p~!?  ...  A notion of first order trace congruence over such terms is introduced and used to show that no finite set of such equations is sound and complete for any reasonable equivalence finer than trace equivalence  ...  Acknowledgements The author would like to thank Zoltan fisik, Wan Fokkink, Ole Jensen and Robin Milner for discussions on this work, and to acknowledge support from SERC studentship 903 118 19, ESPRIT  ... 
doi:10.1016/s0168-0072(97)00036-5 fatcat:hhx2en7txvdwtemeytcjshzxoe

On the Axiomatisation of Branching Bisimulation Congruence over CCS [article]

Luca Aceto, Valentina Castiglioni, Anna Ingolfsdottir, Bas Luttik
2022 arXiv   pre-print
Firstly, we show that CCS is not finitely based modulo the considered congruence.  ...  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  ...  Nonexistence of a finite axiomatisation We devote this section to proving Theorem 4.  ... 
arXiv:2206.13927v1 fatcat:birxh3whifdcnjkigxppkihgma

Are Two Binary Operators Necessary to Obtain a Finite Axiomatisation of Parallel Composition? [article]

Luca Aceto, Valentina Castiglioni, Wan Fokkink, Anna Igolfsdottir, Bas Luttik
2022 arXiv   pre-print
These results raise the question of whether there is one auxiliary binary operator whose addition to CCS leads to a finite axiomatisation of bisimilarity.  ...  a finite axiomatisation of bisimilarity in the simplified setting cannot satisfy all three assumptions.  ...  Acknowledgements This work has been supported by the project 'Open Problems in the Equational Logic of Processes' (OPEL) of the Icelandic Research Fund (grant No. 196050-051).  ... 
arXiv:2010.01943v3 fatcat:amb557aofbeincutk4s26l36la

CCS with priority guards

Iain Phillips
2008 The Journal of Logic and Algebraic Programming  
We introduce a new approach, involving the addition of "priority guards" to Milner's process calculus CCS.  ...  It has long been recognised that standard process algebra has difficulty dealing with actions of different priority, such as for instance an interrupt action of high priority.  ...  for helpful discussions and suggestions.  ... 
doi:10.1016/j.jlap.2007.06.005 fatcat:cyftbojidzakpnzifckn7kjvim

CCS with Priority Guards [chapter]

Iain Phillips
2001 Lecture Notes in Computer Science  
We introduce a new approach, involving the addition of "priority guards" to Milner's process calculus CCS.  ...  It has long been recognised that standard process algebra has difficulty dealing with actions of different priority, such as for instance an interrupt action of high priority.  ...  for helpful discussions and suggestions.  ... 
doi:10.1007/3-540-44685-0_21 fatcat:ricaqo4dzzgwbfelcaqznd24lu

Page 1030 of Mathematical Reviews Vol. , Issue 92b [page]

1992 Mathematical Reviews  
Tofts, Reactive, gen- erative, and stratified models of probabilistic processes (pp. 130- 141); Faron Moller, The nonexistence of finite axiomatisations for CCS congruences (pp. 142-153); Phokion G.  ...  Tiuryn, Type reconstruction in finite- rank fragments of the polymorphic A-calculus (extended abstract) (pp. 2-11); Edmund Robinson and Giuseppe Rosolini, Polymor- phism, set theory, and call-by-value  ... 

On Finite Bases for Weak Semantics: Failures Versus Impossible Futures [chapter]

Taolue Chen, Wan Fokkink, Rob van Glabbeek
2009 Lecture Notes in Computer Science  
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.  ...  For convergent processes, it coincides with testing semantics [8, 19] , and thus is the coarsest congruence for the CCS parallel composition that respects deadlock behavior.  ... 
doi:10.1007/978-3-540-95891-8_18 fatcat:ynvasvxm3bakjaldybqfncjpwi

Process algebra with prepositional signals

J.C.M. Baeten, J.A. Bergstra
1997 Theoretical Computer Science  
A process in a parallel composition may proceed conditionally, dependent on the presence of a signal in the process in parallel. This allows a natural treatment of signal observation.  ...  Acknowledgements Helpful remarks by the anonymous referees, Jan Joris Vereijken (Eindhoven University of Technology) and Joris Boselie, Leon Moonen (University of Amsterdam) are appreciated.  ...  Basic process algebra with propositional signals BPA with inaction and nonexistence Let A be a finite set. The elements of A will be called atomic actions.  ... 
doi:10.1016/s0304-3975(96)00253-8 fatcat:2ekg34a2z5eg3g46ce3nqt2q6i

A Distribution Law for CCS and a New Congruence Result for the π-Calculus [chapter]

Daniel Hirschkoff, Damien Pous
Foundations of Software Science and Computational Structures  
This axiomatisation is then used to derive congruence of strong bisimilarity in the finite π-calculus in absence of sum.  ...  We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator.  ...  We are grateful to Arnaud Carayol for interesting discussions at early stages of this work.  ... 
doi:10.1007/978-3-540-71389-0_17 dblp:conf/fossacs/HirschkoffP07 fatcat:3maq2lmdcjcwfiqczw4q3oxgxa

Subject index volumes 1–200

1999 Theoretical Computer Science  
of codes, 1105 congruence quotients, 1097 intersection for HDOL sequences, 198 Kleen semigroups, 1583 semigroups, Restivo's condition for -, 886 finiteness problems, 2558 finiteness question for  ...  nets, 2373 finite power property for context-free languages, 3 12 decidability of the -, 3 12 finite prefix code, 142, 630 finite prefix codes, 2108, 2550 monoid of -, 2108 finite presentations  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Is Observational Congruence Axiomatisable in Equational Horn Logic? [chapter]

Michael Mendler, Gerald Lüttgen
Lecture Notes in Computer Science  
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  ...  This paper presents a positive and a negative result regarding axiomatisability of observational congruence in equational Horn logic.  ...  As our first technical result, we provide an axiomatisation of observational congruence for finite state processes which is in pure equational Horn form.  ... 
doi:10.1007/978-3-540-74407-8_14 fatcat:dbi6wknv4vccznj2zxetg5uphm

Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?

Luca Aceto, Valentina Castiglioni, Wan Fokkink, Anna Ingólfsdóttir, Bas Luttik, Christel Baier, Jean Goubault-Larrecq
2021
These results raise the question of whether there is one auxiliary binary operator whose addition to CCS leads to a finite axiomatisation of bisimilarity.  ...  Bergstra and Klop have shown that bisimilarity has a finite equational axiomatisation over ACP/CCS extended with the binary left and communication merge operators.  ...  ā , L f τ In this section we discuss the nonexistence of a finite axiomatisation of CCS f in the case of an operator f that, modulo bisimilarity, distributes over summation in one of its arguments.  ... 
doi:10.4230/lipics.csl.2021.8 fatcat:xkfcr5npdfes7he4uffxd4oaky

Page 1328 of Mathematical Reviews Vol. 24, Issue Index [page]

Mathematical Reviews  
(see 92i:68005) — Specifying concurrent objects as communicating processes. 92i:68100 Moller, Faron The nonexistence of finite axiomatisations for CCS congruences. (see 92b:68007) Morgan, C.  ...  . * On the shape of mathematical arguments. 92f:68109 Gil-Luezas, Ana A verification system for functional programming languages.  ... 
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