## Syntactic formats for free: An abstract approach to process equivalence (2003)

Venue: | in: Proc. CONCUR 2003, LNCS 2761 (2003 |

Citations: | 8 - 6 self |

### BibTeX

@INPROCEEDINGS{Klin03syntacticformats,

author = {Bartek Klin},

title = {Syntactic formats for free: An abstract approach to process equivalence},

booktitle = {in: Proc. CONCUR 2003, LNCS 2761 (2003},

year = {2003},

pages = {72--86},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. A framework of Plotkin and Turi’s, originally aimed at providing an abstract notion of bisimulation, is modified to cover other operational equivalences and preorders. Combined with bialgebraic methods, it yields a technique for the derivation of syntactic formats for transition system specifications which guarantee that various operational preorders are precongruences. The technique is applied to the trace preorder, the completed trace preorder and the failures preorder. In the latter two cases, new syntactic formats guaranteeing precongruence properties are introduced. 1

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Citation Context ...operational equivalences and preorders have been defined on processes. Among these are: bisimulation equivalence [19], simulation preorder, trace preorder, completed trace preorder, failures preorder =-=[13,23]-=- and many others (for a comprehensive list see [10]). In the case of processes without internal actions, all of the above have been given modal characterisations [10], obtained by considering appropri... |

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Citation Context ...ompleted trace preorder and the failures preorder. In the latter two cases, new syntactic formats guaranteeing precongruence properties are introduced. 1 Introduction Structural operational semantics =-=[21,2]-=- is one of the most fundamental frameworks for providing a precise interpretation of programming and specification languages. Due to its flexibility and generality, it has gained much popularity in th... |

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Citation Context ...ed on processes. Among these are: bisimulation equivalence [19], simulation preorder, trace preorder, completed trace preorder, failures preorder [13,23] and many others (for a comprehensive list see =-=[10]-=-). In the case of processes without internal actions, all of the above have been given modal characterisations [10], obtained by considering appropriate subsets of the Hennessy-Milner logic [12]. Reas... |

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Citation Context ...is to impose syntactic restrictions (called syntactic formats) on operational rules. Many such formats have been developed. For bisimulation equivalence, the examples are: de Simone format [27], GSOS =-=[8]-=-, and ntyft/ntyxt [11], each of these generalising the previous one. For trace equivalence, examples include [31,5], while several versions of decorated trace preorders have been provided with formats... |

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Citation Context ... The search for an abstract theory of processes, bisimulation and ’well-behaved’ operational semantics has led to development of final coalgebra semantics [24], and — later — of bialgebraic semantics =-=[29,30]-=- of processes. In these frameworks, the notion of a transition system is parametrised by a notion of behaviour. Bisimulation is modelled abstractly as a span of coalgebra morphisms. The abstract notio... |

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Citation Context ...f(A × −)-coalgebras and Pf(A × −)-coalgebra morphisms. The carrier S of this coalgebra may be described as the set of synchronisation trees with edges having labels from A, quotiented by bisimulation =-=[4, 29]-=-. In the following we specialise the framework of [30] to the category Set and behaviour functor Pf(A × −). Any syntactic signature Σ determines a so-called syntactic endofunctor Σ : Set → Set which a... |

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Citation Context ...ompleted trace preorder and the failures preorder. In the latter two cases, new syntactic formats guaranteeing precongruence properties are introduced. 1 Introduction Structural operational semantics =-=[21,2]-=- is one of the most fundamental frameworks for providing a precise interpretation of programming and specification languages. Due to its flexibility and generality, it has gained much popularity in th... |

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Citation Context ...of the functor Pf(A × −), and to give a (classical) bisimulation relation is to give a span of coalgebra morphisms for this functor [3, 24]. Another abstract approach to bisimulation is via open maps =-=[15]-=-. In [29,30] it was shown how to define operational rules on an abstract level. For abstract transition system specifications defined in this way, bisimulation equivalence (defined abstractly, using s... |

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Citation Context ... have been provided with formats in [6]. For an overview of the subject see [2]. Another approach which generates LTS on which bisimulation is a congruence is the smallest-contexts-as-labels approach =-=[26,18,25]-=-. The search for an abstract theory of processes, bisimulation and ’well-behaved’ operational semantics has led to development of final coalgebra semantics [24], and — later — of bialgebraic semantics... |

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Citation Context ...c restrictions (called syntactic formats) on operational rules. Many such formats have been developed. For bisimulation equivalence, the examples are: de Simone format [27], GSOS [8], and ntyft/ntyxt =-=[11]-=-, each of these generalising the previous one. For trace equivalence, examples include [31,5], while several versions of decorated trace preorders have been provided with formats in [6]. For an overvi... |

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Citation Context ... (and respective equivalences). This constitutes another systematic approach to operational preorders and equivalences, such as those based on testing scenarios [10], modal logics [10], and quantales =-=[1]-=-. Although the framework is general, in this paper we shall concentrate on the category of sets and functions, Set. We define the test-suite fibration with total 2scategory Set ∗ having as objects pai... |

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Citation Context ... have been provided with formats in [6]. For an overview of the subject see [2]. Another approach which generates LTS on which bisimulation is a congruence is the smallest-contexts-as-labels approach =-=[26,18,25]-=-. The search for an abstract theory of processes, bisimulation and ’well-behaved’ operational semantics has led to development of final coalgebra semantics [24], and — later — of bialgebraic semantics... |

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Citation Context ...properties is to impose syntactic restrictions (called syntactic formats) on operational rules. Many such formats have been developed. For bisimulation equivalence, the examples are: de Simone format =-=[27]-=-, GSOS [8], and ntyft/ntyxt [11], each of these generalising the previous one. For trace equivalence, examples include [31,5], while several versions of decorated trace preorders have been provided wi... |

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Citation Context ...llest-contexts-as-labels approach [26,18,25]. The search for an abstract theory of processes, bisimulation and ’well-behaved’ operational semantics has led to development of final coalgebra semantics =-=[24]-=-, and — later — of bialgebraic semantics [29,30] of processes. In these frameworks, the notion of a transition system is parametrised by a notion of behaviour. Bisimulation is modelled abstractly as a... |

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Citation Context ...be extended to deal with other operational preorders and equivalences described in literature. Secondly, one can move from the GSOS format (and its subformats) to the more general (safe) ntree format =-=[9]-=-, which can also be formalised in the bialgebraic framework [30]. Thirdly, the abstract framework of test suites seems to be general enough to cover other notions of process behaviour (e.g. involving ... |

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Citation Context ... The search for an abstract theory of processes, bisimulation and ’well-behaved’ operational semantics has led to development of final coalgebra semantics [24], and — later — of bialgebraic semantics =-=[29,30]-=- of processes. In these frameworks, the notion of a transition system is parametrised by a notion of behaviour. Bisimulation is modelled abstractly as a span of coalgebra morphisms. The abstract notio... |

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Categorical Logic and Type Theory, volume 141
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Citation Context ...t τ ⊆ PX, the specialisation preorder of τ is defined by x ≤τ x ′ iff ∀V ∈ τ. x ∈ V ⇒ x ′ ∈ V For an introduction to fibrations and related terminology, the reader is referred to the first chapter of =-=[14]-=-. Definition 11 (Test suite). A test on a set X is a function V : X → 2. We say that an element x passes a test V iff V x = tt. A test suite on X is a collection of tests on X which includes the maxim... |

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Citation Context ...ly renamed) rule ρ ∈ R a with the conclusion f(x1, . . . ,xn) ◮t such that for each premise r of ρ there exists an i ∈ {1, . . .,k} such that r completes pi. Proposition 6. BPA is in Fl-format. ⊓⊔ In =-=[7]-=- it was shown that the failures preorder is not a precongruence for BPA extended with sequential composition. Proposition 7. If A contains at least two different labels a, b, then BPA extended with se... |

13 | Deriving bisimulation congruences: a 2categorical approach
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Citation Context ... have been provided with formats in [6]. For an overview of the subject see [2]. Another approach which generates LTS on which bisimulation is a congruence is the smallest-contexts-as-labels approach =-=[26,18,25]-=-. The search for an abstract theory of processes, bisimulation and ’well-behaved’ operational semantics has led to development of final coalgebra semantics [24], and — later — of bialgebraic semantics... |

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Citation Context ...e following, P : Set → Set will denote the (covariant) powerset functor. The (covariant) finite powerset functor Pf : Set → Set takes a set to the set of its finite subsets. The reader is referred to =-=[17]-=- for any unexplained categorical notation used henceforward. There is a bijection between the set of finitely branching LTS over a fixed set of actions A and the coalgebras of the functor Pf(A × −). I... |

5 |
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Citation Context ... developed. For bisimulation equivalence, the examples are: de Simone format [27], GSOS [8], and ntyft/ntyxt [11], each of these generalising the previous one. For trace equivalence, examples include =-=[31,5]-=-, while several versions of decorated trace preorders have been provided with formats in [6]. For an overview of the subject see [2]. Another approach which generates LTS on which bisimulation is a co... |

4 | Precongruence formats for decorated trace preorders
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Citation Context ...d ntyft/ntyxt [11], each of these generalising the previous one. For trace equivalence, examples include [31,5], while several versions of decorated trace preorders have been provided with formats in =-=[6]-=-. For an overview of the subject see [2]. Another approach which generates LTS on which bisimulation is a congruence is the smallest-contexts-as-labels approach [26,18,25]. The search for an abstract ... |

3 |
Bialgebraic semantics and recursion (extended abstract
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Citation Context ...dofunctor Pf(A × −), the abstract operational rules specialise to GSOS rules. The abstract framework which defines bisimulation as a span of coalgebra morphisms is not sufficient for certain purposes =-=[22]-=- and in particular one runs into problems when working with complete partial orders. Recently, another abstract notion of bisimulation, based on topologies (or complete boolean algebras) of tests, has... |

1 |
Bialgebraic semantics (and recursion). Unpublished notes
- Plotkin
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Citation Context ...lar one runs into problems when working with complete partial orders. Recently, another abstract notion of bisimulation, based on topologies (or complete boolean algebras) of tests, has been proposed =-=[20,28]-=-. Again, for the familiar process behaviour the novel abstract notion is equivalent to the classical one. In this paper we show that the latter abstract definition of bisimulation can in fact be modif... |

1 |
Fibrations and bisimulation. Unpublished notes
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(Show Context)
Citation Context ...lar one runs into problems when working with complete partial orders. Recently, another abstract notion of bisimulation, based on topologies (or complete boolean algebras) of tests, has been proposed =-=[20,28]-=-. Again, for the familiar process behaviour the novel abstract notion is equivalent to the classical one. In this paper we show that the latter abstract definition of bisimulation can in fact be modif... |

1 | Bialgebraic semantics and recursion
- Plotkin
- 2001
(Show Context)
Citation Context ...n of coalgebra morphisms is not sufficient for certain purposes [19]. Recently, another abstract notion of bisimulation, based on topologies (or complete boolean algebras) of tests, has been proposed =-=[20, 24]-=-. In this paper we show that the latter abstract definition of bisimulation can be modified in a structured manner, to yield other known equivalences and preorders. We illustrate this approach on trac... |