A finite equational base for CCS with left merge and communication merge

Aceto, Luca; Fokkink, Wan; Ingólfsdóttir, Anna; Luttik, Bas

doi:10.1145/1459010.1459016

Cited by 12 publications

(8 citation statements)

References 20 publications

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“…Recall that, by one of the assumptions of the proposition, σ (u) ↔ f (α, p n ), and thus σ (u) has depth n + 2. However, by Equation (10),…”

Section: Proving Theorem 81mentioning

confidence: 99%

“…Bergstra and Klop showed in Reference [19] that a finite ground-complete axiomatisation modulo bisimilarity can be obtained by enriching CCS with two auxiliary operators, namely, the left merge and the communication merge |, expressing, respectively, one step in the asymmetric pure interleaving and the synchronous behaviour of . Their result was then strengthened by Aceto et al in Reference [10], where it is proved that, over the fragment of CCS without recursion, restriction, and relabelling, the auxiliary operators and | allow for finitely axiomatising modulo bisimilarity also when CCS terms with variables are considered. Moreover, in Reference [14], that result is extended to the fragment of CCS with relabelling and restriction, but without communication.…”

Section: Introductionmentioning

confidence: 97%

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

Aceto

Castiglioni

Fokkink

et al. 2022

ACM Trans. Comput. Logic

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Bergstra and Klop have shown that bisimilarity has a finite equational axiomatisation over ACP/CCS extended with the binary left and communication merge operators. 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. We contribute to answering this question in the simplified setting of the recursion-, relabelling-, and restriction-free fragment of CCS. 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 a finite axiomatisation of bisimilarity in the simplified setting cannot satisfy all three assumptions.

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“…Recall that, by one of the assumptions of the proposition, σ (u) ↔ f (α, p n ), and thus σ (u) has depth n + 2. However, by Equation (10),…”

Section: Proving Theorem 81mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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

Aceto

Castiglioni

Fokkink

et al. 2022

ACM Trans. Comput. Logic

Self Cite

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show abstract

“…Unique parallel decomposition can be also used to define a notion of normal form. Such a notion of normal form is useful in completeness proofs for equational axiomatizations in settings in which an elimination theorem for parallel composition is lacking (see, e.g., [1,2,3,9,11]). In [13], UPD is used to prove complete axiomatisation and decidability results in the context of a higher-order process calculus.…”

Section: Introductionmentioning

confidence: 99%

Unique Parallel Decomposition for the Pi-calculus

Lee

Luttik

2016

Electron. Proc. Theor. Comput. Sci.

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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

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“…The article [3] surveys results on the existence of finite, complete equational axiomatizations of behavioural equivalences over fragments of process algebras up to 2005. Some of the results on the (non)existence of finite, complete (in)equational axiomatizations of behavioural semantics over process algebras that have been obtained since the publication of that survey may be found in [1,2,[4][5][6]8].…”

Section: Introductionmentioning

confidence: 99%