## Hereditary history preserving bisimulation is decidable for trace-labelled systems (2002)

Venue: | In: FSTTCS’02. Volume 2556 of LNCS. (2002) 289–300 |

Citations: | 4 - 0 self |

### BibTeX

@INPROCEEDINGS{Mukund02hereditaryhistory,

author = {Madhavan Mukund},

title = {Hereditary history preserving bisimulation is decidable for trace-labelled systems},

booktitle = {In: FSTTCS’02. Volume 2556 of LNCS. (2002) 289–300},

year = {2002},

pages = {289--300}

}

### OpenURL

### Abstract

Abstract. Hereditary history preserving bisimulation is a natural extension of bisimulation to the setting of so-called “true ” concurrency. Somewhat surprisingly, this extension turns out to be undecidable, in general, for finite-state concurrent systems. In this paper, we show that for a substantial and useful class of finite-state concurrent systems— those whose semantics can be described in terms of Mazurkiewicz traces— hereditary history preserving is decidable. 1

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Citation Context ...hing-time behavioural equivalence known as hereditary history preserving bisimulation. Hereditary history preserving bisimulation is a natural extension of bisimulation, as defined by Park and Milner =-=[11,13]-=-, from a setting where concurrency is equated with nondeterministic interleaving to a richer setting where nondeterminism and concurrency are represented explicitly and independently. Hereditary histo... |

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Citation Context ...hing-time behavioural equivalence known as hereditary history preserving bisimulation. Hereditary history preserving bisimulation is a natural extension of bisimulation, as defined by Park and Milner =-=[11,13]-=-, from a setting where concurrency is equated with nondeterministic interleaving to a richer setting where nondeterminism and concurrency are represented explicitly and independently. Hereditary histo... |

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Citation Context ...narczyk [1], but became more well known when it reappeared as a natural construction in a general, categorical approach to nondeterminism and concurrency arising out of the work of Winskel and Nielsen=-=[7,17]-=-. Hereditary history preserving bisimulation requires two concurrent systems to retain the same nondeterministic choices as they evolve, as in conventional bisimulation. In addition, at every state, e... |

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Citation Context ...narczyk [1], but became more well known when it reappeared as a natural construction in a general, categorical approach to nondeterminism and concurrency arising out of the work of Winskel and Nielsen=-=[7,17]-=-. Hereditary history preserving bisimulation requires two concurrent systems to retain the same nondeterministic choices as they evolve, as in conventional bisimulation. In addition, at every state, e... |

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Citation Context ...ce of model is not important: we could have, instead, worked with any other model that has an explicit notion of independence or concurrency built in, such as labelled asynchronous transition systems =-=[2]-=-, asynchronous automata [18] or transition systems with independence [17]. Nets A net is a quadruple (S, T, F, Min) where: – S is a finite, non-empty set of places. – T is a finite, non-empty set of t... |

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Citation Context ... systems—those whose behaviours can be described by Mazurkiewicz traces. Our main result is that hereditary history preserving bisimulation is decidable for this class of systems. Mazurkiewicz traces =-=[10]-=- are labelled partial orders generated by independence alphabets of the form (Σ, I), where I is a static independence relation over Σ. If (a, b) ∈ I, a and b are deemed to be independent actions that ... |

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Citation Context ...dalities. The decidability question was investigated in [5] where some very restricted positive results were obtained. Earlier, a weaker notion of history preserving bisimulation had been proposed in =-=[3, 15,16]-=-. Here, too, the two systems have to progressively simulate each others’ concurrent steps. However, the bisimulation is built up one action at a time, so each interleaving of a concurrent step in one ... |

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Citation Context ...ministic interleaving to a richer setting where nondeterminism and concurrency are represented explicitly and independently. Hereditary history preserving bisimulation was first defined by Bednarczyk =-=[1]-=-, but became more well known when it reappeared as a natural construction in a general, categorical approach to nondeterminism and concurrency arising out of the work of Winskel and Nielsen[7,17]. Her... |

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Citation Context ...bled. Traces are a natural formalism for describing the behaviour of various static networks of communicating finite-state agents as modelled by Petri nets [14] or communicating finite-state automata =-=[18]-=-. Hence, our positive result is applicable to a substantial and useful subclass of finite-state concurrent systems. The paper is organized as follows. We begin with some basic definitions about labell... |

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Citation Context ...dalities. The decidability question was investigated in [5] where some very restricted positive results were obtained. Earlier, a weaker notion of history preserving bisimulation had been proposed in =-=[3, 15,16]-=-. Here, too, the two systems have to progressively simulate each others’ concurrent steps. However, the bisimulation is built up one action at a time, so each interleaving of a concurrent step in one ... |

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Citation Context .... Then, ρ(w) � ρ(w′ ). We omit the proof this result, which is a reformulation of a standard result of trace theory that any linearization of a trace fixes its underlying partial order representation =-=[4]-=-. Observe that the nets in Figure 2 are not trace-labelled. For instance, in the net on the left, the transition sequences t1t3t5 and t2t3t4 both generate the same labelled sequence, abc, but give ris... |

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Citation Context ... system. Thus, from the standpoint of faithfully preserving concurrency and nondeterminism, this notion is slightly unsatisfactory. The decidability of this variety of bisimulation was established in =-=[6]-=-. In this paper, we examine the decidability question afresh for a restricted class of concurrent systems—those whose behaviours can be described by Mazurkiewicz traces. Our main result is that heredi... |

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Citation Context .... In [12], a game-theoretic formulation is presented, along with a characterization in terms of a Hennessy-Milner style modal logic with past modalities. The decidability question was investigated in =-=[5]-=- where some very restricted positive results were obtained. Earlier, a weaker notion of history preserving bisimulation had been proposed in [3, 15,16]. Here, too, the two systems have to progressivel... |

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Citation Context ...gh this seems to be a fairly innocuous extension, the repercussions are quite severe. It turns out that history preserving bisimulation is, in general, undecidable for finite-state concurrent systems =-=[8]-=-. ⋆ Partially supported by IFCPAR Project 2102-1 (ACSMV).s290 A few positive results have been obtained regarding hereditary history preserving bisimulation. In [12], a game-theoretic formulation is p... |

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Citation Context ...for finite-state concurrent systems [8]. ⋆ Partially supported by IFCPAR Project 2102-1 (ACSMV).s290 A few positive results have been obtained regarding hereditary history preserving bisimulation. In =-=[12]-=-, a game-theoretic formulation is presented, along with a characterization in terms of a Hennessy-Milner style modal logic with past modalities. The decidability question was investigated in [5] where... |

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Citation Context ...ions in such a way that every step can be broken up into all possible substeps. This definition of step transition systems is equivalent to deterministic distributed transition systems, as defined in =-=[9]-=-. Notice that for independent actions a and b, it is possible to have transitions δ(q, a) = qa, δ(q, b) = qb and δ(qa, b) = δ(qb, a) = q ′ , but not have the step transition δ(q, {a, b}) = q ′ . A ste... |

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Citation Context ...dalities. The decidability question was investigated in [5] where some very restricted positive results were obtained. Earlier, a weaker notion of history preserving bisimulation had been proposed in =-=[3, 15,16]-=-. Here, too, the two systems have to progressively simulate each others’ concurrent steps. However, the bisimulation is built up one action at a time, so each interleaving of a concurrent step in one ... |