## Ready to preorder: get your BCCSP axiomatization for free (2007)

Venue: | Proceedings of CALCO’07, volume 4624 of LNCS |

Citations: | 13 - 3 self |

### BibTeX

@INPROCEEDINGS{Aceto07readyto,

author = {Luca Aceto and Wan Fokkink and Anna Ingolfsdottir},

title = {Ready to preorder: get your BCCSP axiomatization for free},

booktitle = {Proceedings of CALCO’07, volume 4624 of LNCS},

year = {2007},

pages = {65--79},

publisher = {Springer}

}

### OpenURL

### Abstract

Abstract. This paper contributes to the study of the equational theory of the semantics in van Glabbeek’s linear time- branching time spectrum over the language BCCSP, a basic process algebra for the description of finite synchronization trees. It offers an algorithm for producing a complete (respectively, ground-complete) equational axiomatization of any behavioral congruence lying between ready simulation equivalence and partial traces equivalence from a complete (respectively, ground-complete) inequational axiomatization of its underlying precongruence—that is, of the precongruence whose kernel is the equivalence. The algorithm preserves finiteness of the axiomatization when the set of actions is finite. 1

### Citations

3643 | Communicating Sequential Processes
- Hoare
- 1985
(Show Context)
Citation Context ... decorated traces. Van Glabbeek [13] studied the semantics in his spectrum in the setting of the process algebra BCCSP, which contains only the basic process algebraic operators from CCS [18] and CSP =-=[17]-=-, but is sufficiently powerful to express all finite synchronization trees. In the aforementioned reference, van Glabbeek gave, amongst a wealth of other results, (in)equational axiomatizations for th... |

3430 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...otions and on decorated traces. Van Glabbeek [13] studied the semantics in his spectrum in the setting of the process algebra BCCSP, which contains only the basic process algebraic operators from CCS =-=[18]-=- and CSP [17], but is sufficiently powerful to express all finite synchronization trees. In the aforementioned reference, van Glabbeek gave, amongst a wealth of other results, (in)equational axiomatiz... |

517 | Algebraic Laws for Nondeterminism and Concurrency
- Hennessy, Milner
- 1985
(Show Context)
Citation Context ...tion E for BCCSP modulo a preorder in the linear time - branching time spectrum that includes the ready simulation preorder. Without loss of generality, we assume that the four classic equations from =-=[16]-=- that completely axiomatize bisimulation equivalence [18] are contained in E, and that so do the defining inequational axioms for ready simulation forseach action a: ax � ax + ay . The axiomatization ... |

201 |
Bisimulation can’t be traced
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...a companion to [1]. That paper offered an algorithm that generates a finite, ground-complete axiomatization for bisimulation equivalence from an operational specification of a language in GSOS format =-=[7]-=-. That procedure relies on the axiomatization of bisimulation equivalence over the language BCCSP. Here we have focused on the algorithmic generation of complete axiomatizations for other equivalences... |

201 |
Structured operational semantics and bisimulation as a congruence
- Groote, Vaandrager
- 1992
(Show Context)
Citation Context ...orem 5.1 of [12], our results apply to ω-complete as well as to ground-complete axiomatizations. It would be interesting to extend our algorithm so that it applies also to nested simulation semantics =-=[15]-=- and to possible futures semantics [20]. However, as shown in [2], unlike the semantics we have considered in this study, nested simulation and possible futures semantics afford no finite ground-compl... |

102 | The linear time – branching time spectrum I; the semantics of concrete, sequential processes - Glabbeek - 2001 |

91 | Turning SOS rules into equations
- Aceto, Bloom, et al.
- 1994
(Show Context)
Citation Context ...axiomatizations that are automatically generated by our algorithm are very similar, when not identical, to those presented in the literature. In this respect, this study may be seen as a companion to =-=[1]-=-. That paper offered an algorithm that generates a finite, ground-complete axiomatization for bisimulation equivalence from an operational specification of a language in GSOS format [7]. That procedur... |

52 |
Axioms for Concurrency
- Moller
- 1989
(Show Context)
Citation Context ...s possible worlds ready traces failures completed traces traces readies Fig. 1. The linear time - branching time spectrum possible futures The core axioms A1–4 for BCCSP(A) given below are ω-complete =-=[19]-=-, and sound and ground-complete [16, 18] modulo bisimulation equivalence, which is the finest semantics in the linear time - branching time spectrum. A1 x + y ≈ y + x A2 (x + y) + z ≈ x + (y + z) A3 x... |

29 | Finite equational bases in process algebra: Results and open questions - Aceto, Fokkink, et al. - 2005 |

25 |
A new strategy for proving ω-completeness with applications in process algebra
- Groote
- 1990
(Show Context)
Citation Context ... for the preorders and equivalences in the spectrum, such that two closed BCCSP terms can be equated by the axioms if, and only if, they are related by the preorder or equivalence in question. Groote =-=[14]-=- obtained ω-completeness results for most of ⋆ The first and third author were partly supported by the project “The Equational Logic of Parallel Processes” (nr. 060013021) of The Icelandic Research Fu... |

24 | A menagerie of non-finitely based process semantics over BPA*—from ready simulation to completed traces
- Aceto, Fokkink, et al.
- 1998
(Show Context)
Citation Context ...P(A) terms.) Lemma 1. If t + x � u, and either � ⊆ �CT, or � ⊆ �PT and |A| > 1, then x is a summand of u. If |A| = 1, then the partial traces preorder and the simulation preorder coincide— see, e.g., =-=[3]-=-. For this special case, Lemma 1 fails. Namely, let A = {a}. Then x � ax is sound for the partial traces (and simulation) preorder. Lemma 2. Let � be an equivalence in the linear time - branching time... |

19 |
Possible futures, acceptances, refusals and communicating processes
- Rounds, Brookes
- 1981
(Show Context)
Citation Context ...ω-complete as well as to ground-complete axiomatizations. It would be interesting to extend our algorithm so that it applies also to nested simulation semantics [15] and to possible futures semantics =-=[20]-=-. However, as shown in [2], unlike the semantics we have considered in this study, nested simulation and possible futures semantics afford no finite ground-complete axiomatization over BCCSP even in t... |

17 | On the axiomatizability of ready traces, ready simulation and failure traces
- Blom, Fokkink, et al.
- 2003
(Show Context)
Citation Context ...the presence of an infinite collection of actions. Remark 1. Since ax � ax + ay is assumed to be present in E for each a ∈ A, by step B of the algorithm, the defining axioms for ready simulation from =-=[6]-=-, namely b(ax + z) + b(ax + ay + z) ≈ b(ax + ay + z) , are present in A(E), for all a, b ∈ A. We are now ready to present the main result of the paper to the effect that the algorithm defined above de... |

15 | Nested semantics over finite trees are equationally hard
- Aceto, Fokkink, et al.
- 2004
(Show Context)
Citation Context ...ound-complete axiomatizations. It would be interesting to extend our algorithm so that it applies also to nested simulation semantics [15] and to possible futures semantics [20]. However, as shown in =-=[2]-=-, unlike the semantics we have considered in this study, nested simulation and possible futures semantics afford no finite ground-complete axiomatization over BCCSP even in the presence of a single ac... |

9 | A finite basis for failure semantics
- Fokkink, Nain
- 2005
(Show Context)
Citation Context ...ivalence if E is ω-complete (respectively, ground-complete) for the preorder (Theorem 1). The proof of this statement is non-trivial, and relies on a careful analysis of the so-called cover equations =-=[10]-=- for the semantics in the linear time - branching time spectrum we consider in this study. Cover equations give us an explicit description of the equational theory for a particular semantics in terms ... |

5 | On finite alphabets and infinite bases III: Simulation - Chen, Fokkink - 2006 |

5 |
Bisimulations Up-to for the Linear Time Branching Time Spectrum
- Frutos-Escrig, Gregorio-Rodríguez
- 2005
(Show Context)
Citation Context ...alences in the spectrum over the language BCCSP. 13s14 The spirit of our study is also very similar to the one in [12]. In that reference, independent of our work and building on their previous paper =-=[11]-=-, de FrutosEscrig and Gregorio-Rodríguez show, amongst other things, how to generate an inequational axiomatization for preorders in the spectrum from equational axiomatizations for the corresponding ... |

3 | On finite alphabets and infinite bases II: Completed and ready simulation - Chen, Fokkink, et al. - 2006 |

2 |
Simulations up-to and canonical preorders (extended abstract
- Frutos-Escrig, Gregorio-Rodríguez
- 2007
(Show Context)
Citation Context ...have focused on the algorithmic generation of complete axiomatizations for other equivalences in the spectrum over the language BCCSP. 13s14 The spirit of our study is also very similar to the one in =-=[12]-=-. In that reference, independent of our work and building on their previous paper [11], de FrutosEscrig and Gregorio-Rodríguez show, amongst other things, how to generate an inequational axiomatizatio... |