## Higher dimensional transition systems (1996)

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Citations: | 25 - 3 self |

### BibTeX

@INPROCEEDINGS{Cattani96higherdimensional,

author = {Gian Luca Cattani},

title = {Higher dimensional transition systems},

booktitle = {},

year = {1996},

pages = {55--62},

publisher = {Press}

}

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### Abstract

We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elemen-tary, set-theoretic formalisation of the idea of higher di-mensional transition. We show an embedding of the cate-gory of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equiv-alence when we restrict to non-degenerate automata. More-ovel; we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history pre-serving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we dejine a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures.

### Citations

265 |
Event structures
- Winskel
- 1987
(Show Context)
Citation Context ...the interleaved occurrence of independent actions. The category Petri of Petri nets [9] embeds in HDTS via the standard case graph construction. The domain of configurations of prime event structures =-=[13]-=- defines an obvious embedding EvStr L) HDTS that has a reflection left adjoint. Analogously, configuration structures [3,4] embed reflectively in HDTS, provided we equip them with the natural notion o... |

265 | chapter Models for concurrency - Winskel, Nielsen - 1995 |

166 |
Petri nets are monoids
- Meseguer, Montanari
- 1990
(Show Context)
Citation Context ...ith independence, there exists an embedding TSI L) HDTS that adds all the higher dimensional transitions induced by the interleaved occurrence of independent actions. The category Petri of Petri nets =-=[9]-=- embeds in HDTS via the standard case graph construction. The domain of configurations of prime event structures [13] defines an obvious embedding EvStr L) HDTS that has a reflection left adjoint. Ana... |

127 | Modeling concurrency with geometry
- Pratt
- 1991
(Show Context)
Citation Context ... via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures. Introduction In =-=[11]-=-, Pratt argued in favour of generalising transition systems to models able to represent concurrent systems faithfully enough. In particular, he advocates for a transitionbased model in which the concu... |

118 | Bisimulation from open maps
- Joyal, Nielsen, et al.
- 1996
(Show Context)
Citation Context ...eneralised event structures, called higher dimensional event structures, which is proved equivalent to OH DTS. Considering a corresponding generalisation of the strong history preserving bisimulation =-=[8]-=-, we prove that, remarkably, it coincides under the equivalence oHDTS 2 HDES with the bisimulation defined in Section 1 for HDTS. This, together with the fact that the unfolding HDTS -+ oHDTS preserve... |

43 | Homology of higher-dimensional automata
- Goubault, Jensen
- 1992
(Show Context)
Citation Context ...tially advocated for. Moreover, higher dimensional automata include ‘degenerate’ structures which fail the original computational intuition. Taking up van Glabbeek’s framework, Goubauit and Jensen in =-=[6,5]-=- proposed to use structures and methods derived from algebraic topology, most notably the chain bicomplexes of 161. Although the precise relationships between higher dimensional automata and bicomplex... |

43 | Petri nets and step transition systems
- Mukund
- 1992
(Show Context)
Citation Context ...s of partial maps on events and labels that preserve configurations and respect the relabelling. Moreover, HDTS can be seen as a full subcategory of the category STS of the step transition systems of =-=[10] and-=- bears a seemingly close relationship, not yet fully understood, to local event structures [7]. Definition 1.3 (Paths and Runs) A path in a hdts is a sequence of contiguous transitions (s 0 ; �� 1... |

40 | Configuration structures
- Glabbeek, Plotkin
- 1995
(Show Context)
Citation Context ...se graph construction. The domain of configurations of prime event structures [13] defines an obvious embedding EvStr L) HDTS that has a reflection left adjoint. Analogously, configuration structures =-=[3,4]-=- embed reflectively in HDTS, provided we equip them with the natural notion of morphism: pairs of partial maps on events and labels that preserve configurations and respect the relabelling. T2 57 More... |

34 |
Refinement of actions in causality based models
- Glabbeek, Goltz
- 1990
(Show Context)
Citation Context ...se graph construction. The domain of configurations of prime event structures [13] defines an obvious embedding EvStr L) HDTS that has a reflection left adjoint. Analogously, configuration structures =-=[3,4]-=- embed reflectively in HDTS, provided we equip them with the natural notion of morphism: pairs of partial maps on events and labels that preserve configurations and respect the relabelling. T2 57 More... |

20 |
Bisimulations for higher dimensional automata. Email message sent to the Concurrence mailing list on July 7
- Glabbeek
- 1991
(Show Context)
Citation Context ... actions. Observing that, after all, n-cells do not accommodate higher dimensional transitions so well, most notably because of a mismatch of the respective notions of source and target, van Glabbeek =-=[2]-=- proposed the notion higher dimensional automata as a simpler, more fitting formalisation of Pratt’s idea. However, in such automata, higher dimensional transitions represent lists rather than sets of... |

16 |
Models for concurrency: Towards a classification. Theoretical Computer Science
- Sassone, Nielsen, et al.
- 1996
(Show Context)
Citation Context ... Higher Dimensional Wansition Systems In order to reveal the events occurring in the runs of a hdts and their interactions, we develop here, in complete analogy with the corresponding results for TSI =-=[12]-=-, the notion of unfolding of hdts to suitable structures. Definition 3.1 (Occurrence HDTS) An occurrence hdts is a hdts that is reachable, acyclic and such that for any pair of transitions (s’,p,s) an... |

8 |
Local event structures and Petri nets
- Hoogers, Kleijn, et al.
- 1993
(Show Context)
Citation Context ...eover, HDTS can be seen as a full subcategory of the category STS of the step transition systems of [ 101 and bears a seemingly close relationship, not yet fully understood, to local event structures =-=[7]-=-. Definition 1.3 (Paths and Runs) A path in a hdts is a sequence of contiguous transitions (~o,,u~,sI)(sI,,u~,s~)..’(s~-I,,u~,s~). A run is a path that originates from the initial state. Building on t... |

1 | Open Maps (at) Work, BRICS Report Series RS-95-23 - CHENG, NIELSEN - 1995 |

1 | Nets and Step Transition Systems. International Joumal of Foundations of - Petri |