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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
Moller proved that auxiliary operators are necessary to obtain a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that this remains true when Hennessy's merge is added to that language  ...  We formulate three natural assumptions pertaining to the operational semantics of auxiliary operators and their relationship to parallel composition, and prove that an auxiliary binary operator facilitating  ...  operators in the finite axiomatisation of parallel composition modulo bisimilarity.  ... 
arXiv:2010.01943v3 fatcat:amb557aofbeincutk4s26l36la

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
Moller proved that auxiliary operators are necessary to obtain a finite axiomatisation of bisimilarity over CCS, and Aceto et al. showed that this remains true when Hennessy's merge is added to that language  ...  These results raise the question of whether there is one auxiliary binary operator whose addition to CCS leads to a finite axiomatisation of bisimilarity.  ...  C S L 2 0 2 1 8:10 Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition? Assumption 3.  ... 
doi:10.4230/lipics.csl.2021.8 fatcat:xkfcr5npdfes7he4uffxd4oaky

On the Axiomatisability of Parallel Composition [article]

Luca Aceto, Valentina Castiglioni, Anna Ingolfsdottir, Bas Luttik, Mathias R. Pedersen
2022 arXiv   pre-print
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  ...  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  ...  We thank Rob van Glabbeek for a fruitful discussion on the axiomatisability of failures equivalence, and the reviewers for their constructive feedback and careful reading of our paper.  ... 
arXiv:2102.11166v5 fatcat:e4cyxjv52zcrvbamh2ps5ylkae

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  
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  ...  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.  ...  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

On sequential composition, action prefixes and process prefix

J. C. M. Baeten, J. A. Bergstra
1994 Formal Aspects of Computing  
Process Prefix In section 3 we added a number of prefix operators. We can generalise this to a setting where the ; operator becomes a binary operator on processes.  ...  The signature of ACP is as follows: This presentation of ACP is an alternative to the presentation in [BW90], where there are two parameters, a finite set of constants A, and a communication function  ... 
doi:10.1007/bf01215407 fatcat:6v4bmxk52bdifj3c6xipemhlhi

Compositional Reasoning for Pointer Structures [chapter]

Yifeng Chen, J. W. Sanders
2006 Lecture Notes in Computer Science  
A parameterised binary combinator is defined that enables important properties (like acyclicity, canonicity and reachability) to be defined in a compositional manner.  ...  A case study is provided to demonstrate how these ideas are used, in the form of rules of Hoare logic, to verify the correctness of an Object-Oriented program.  ...  Acknowledgement The authors are grateful for a variety of refereeing comments that helped them to put the contents of the paper in perspective.  ... 
doi:10.1007/11783596_10 fatcat:x2ixxvynynbm5khpi7kvgpd5wu

Non Axiomatisability of Positive Relation Algebras with Constants, via Graph Homomorphisms

Amina Doumane, Damien Pous, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
We study the equational theories of composition and intersection on binary relations, with or without their associated neutral elements (identity and full relation).  ...  Our proofs exploit a characterisation in terms of graphs and homomorphisms, which we show how to adapt in order to capture standard equational theories over the considered signatures.  ...  Introduction Several operations and constants are used frequently on binary relations: set-theoretic operations (intersection, union, complement, empty and full relations), relational composition and identity  ... 
doi:10.4230/lipics.concur.2020.29 dblp:conf/concur/DoumaneP20 fatcat:y47tza4arjbgxciceilrn5252u

Finite Equational Bases for Fragments of CCS with Restriction and Relabelling [chapter]

Luca Aceto, Anna Ingólfsdóttir, Bas Luttik, Paul van Tilburg
2008 IFIP International Federation for Information Processing  
We present a finite equational base (i.e., a finite ground-complete and omega-complete axiomatisation) for it, including the left merge from ACP as auxiliary operation to facilitate the axiomatisation  ...  The largest fragment we consider includes action prefixing, choice, parallel composition without communication, restriction and relabelling.  ...  Acknowledgements The work of Aceto and Ingólfsdóttir has been partially supported by the projects "The Equational Logic of Parallel Processes" (nr. 060013021) and "New Developments in Operational Semantics  ... 
doi:10.1007/978-0-387-09680-3_22 fatcat:uz2brztgbnd5djxsvrd3law6a4

The algebra of entanglement and the geometry of composition [article]

Amar Hadzihasanovic
2017 arXiv   pre-print
Operations of polygraphs modelled on operations of topological spaces are used as the foundation of a compositional universal algebra, where sliding moves arise from tensor products of polygraphs.  ...  We propose a notion of regular polygraph, barring cell boundaries that are not homeomorphic to a disk of the appropriate dimension.  ...  On the other hand, in order to model, for instance, 0-ary operations of an algebraic theory, it will be necessary to have weak unit cells of the appropriate dimensions.  ... 
arXiv:1709.08086v2 fatcat:ts5oz4iqsnaonfk4m2damc7jyq

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

Generalised Compositional Theories and Diagrammatic Reasoning [article]

Bob Coecke and Ross Duncan and Aleks Kissinger and Quanlong Wang
2015 arXiv   pre-print
The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical  ...  theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.  ...  This operation of parallel combination is called tensor.  ... 
arXiv:1506.03632v1 fatcat:focjnnmp6ffb5nxzhec3sdlgwi

Generalised Compositional Theories and Diagrammatic Reasoning [chapter]

Bob Coecke, Ross Duncan, Aleks Kissinger, Quanlong Wang
2015 Fundamental Theories of Physics  
This operation of parallel combination is called tensor.  ...  In addition to the two operations, composition and tensor, every generalised compositional theory is equipped with certain primitive processes.  ... 
doi:10.1007/978-94-017-7303-4_10 fatcat:ghc4nniggffhhbwa7jgkulicoi

Compositional model checking for linear-time temporal logic [chapter]

Roope Kaivola
1993 Lecture Notes in Computer Science  
There are two versions of the algorithm: one allowing no fairness requirements and one for strongly fair concurrency. Both versions run in time O(IMI" 2':'14'1).  ...  However, due to the state ex. piosion problem modular methods are essential in making the verification task manageable.  ...  definitions of modules and the parallel composition operator.  ... 
doi:10.1007/3-540-56496-9_20 fatcat:mm5byli7efe5deu3lklvtxxege

Turning GSOS Rules into Equations for Linear Time-Branching Time Semantics

M. Gazda, W. Fokkink
2012 Computer journal  
An existing axiomatisation strategy for process algebras modulo bisimulation semantics can be extended so that it can be applied to other behavioural semantics as well.  ...  We study term rewriting properties of the resulting axiomatisations.  ...  Alternative and parallel composition are smooth but not distinctive.  ... 
doi:10.1093/comjnl/bxs120 fatcat:jgal6iw4avckfcbixyc2yxxjnq

Unique parallel decomposition in branching and weak bisimulation semantics

Bas Luttik
2016 Theoretical Computer Science  
First, we show that totally normed behaviours always have parallel decompositions, but that these are not necessarily unique.  ...  Then, we establish that finite behaviours have unique parallel decompositions. We derive the latter result from a general theorem about unique decompositions in partial commutative monoids.  ...  We shall see that the process theories discussed in the previous section give rise to commutative monoids of processes with parallel composition as binary operation.  ... 
doi:10.1016/j.tcs.2015.10.013 fatcat:niqwggevgfazdmvm5oun4ortgi
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