Branching time and orthogonal bisimulation equivalence

Bergstra, Jan A.; Ponse, Alban; Zwaag, Mark B. van der

doi:10.1016/s0304-3975(03)00277-9

Cited by 14 publications

(28 citation statements)

References 20 publications

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“…Bergstra et al in [41] define the notion of orthogonal bisimulation equivalence, which refines van Glabbeek and Weijland's branching bisimulation and allows to collapse a sequence of stuttering steps into one stuttering step to compress internal activity for the purpose of abstraction. The stuttering actions are thus not totally discarded; hence this notion provides a step into the same direction as our approach.…”

Section: Related Workmentioning

confidence: 99%

Next-preserving branching bisimulation

Yatapanage

Winter

2015

Theoretical Computer Science

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Bisimulations are in general equivalence relations between transition systems which assure that certain aspects of the behaviour of the systems are the same. For many applications it is not possible to maintain such an equivalence unless non-observable (stuttering) behaviour is ignored. However, existing bisimulation relations which permit the removal of non-observable behaviour are unable to preserve temporal logic formulas referring to the next step operator. In this paper we propose a novel bisimulation relation, called next-preserving branching bisimulation, which accomplishes this, maintaining the validity of formulas with the next step, while still allowing non-observable behaviour to be reduced. Based on van Glabbeek and Weijland's notion of branching bisimulation with explicit divergence, we define the novel relation for which we prove the preservation of full CTL * . As an example for its application we show how this definition gives rise to an advanced slicing procedure for temporal logics, a technique in which a system model is reduced to a slice which can be used as a substitute in verification and debugging. The result is a novel procedure for generating a slice that is next-preserving branching bisimilar to the original model. Hence, we can assure that any temporal logic property is preserved in a slice that is created with respect to that property, and consequently the verification on the slice is sound.

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Section: Related Workmentioning

confidence: 99%

Next-preserving branching bisimulation

Yatapanage

Winter

2015

Theoretical Computer Science

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“…behaviour at the level of detail where only the actions to be performed and the quantities transferred on performing those actions matter (see also [7]). The axioms of CTC are given in Table 3.…”

Section: Core Tuplix Calculus and Encapsulationmentioning

confidence: 99%

Timed Tuplix Calculus and the Wesseling and van den Bergh Equation

Bergstra¹,

Middelburg²

2013

SACS

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We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant conservation requirement for financial products proposed by Wesseling and van den Bergh by an equation in the framework developed and define a notion of financial product behaviour using this formalization. We also present some properties of financial product behaviours. The development of the framework has been influenced by previous work on the process algebra ACP.

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“…In 2003, Bergstra et al [BPZ03] introduced the notion of orthogonal bisimulation equivalence on labeled transition systems. Orthogonal bisimulation is a refinement of branching bisimulation in which consecutive τ -actions (silent steps) can be compressed into one (but not zero) τ -action.…”

Section: Introductionmentioning

confidence: 99%

“…The main advantage of orthogonal bisimulation, compared to branching bisimulation, is that it combines well with priorities [BPZ03]. Moreover, it has the following nice properties:…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Deciding orthogonal bisimulation

2007

Form. Asp. Comput.

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Abstract. Bergstra, Ponse and van der Zwaag introduced in 2003 the notion of orthogonal bisimulation equivalence on labeled transition systems. This equivalence is a refinement of branching bisimulation, in which consecutive tau's (silent steps) can be compressed into one (but not zero) tau's. The main advantage of orthogonal bisimulation is that it combines well with priorities. Here we solve the problem of deciding orthogonal bisimulation equivalence in finite (regular) labeled transition systems. Unlike as in branching bisimulation, in orthogonal bisimulation, cycles of silent steps cannot be eliminated. Hence, the algorithm of Groote and Vaandrager (1990) cannot be adapted easily. However, we show that it is still possible to decide orthogonal bisimulation with the same complexity as that of Groote and Vaandrager's algorithm. Thus if n is the number of states, and m the number of transitions then it takes O(n(m + n)) time to decide orthogonal bisimilarity on finite labeled transition systems, using O(m + n) space.

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Branching time and orthogonal bisimulation equivalence

Cited by 14 publications

References 20 publications

Next-preserving branching bisimulation

Next-preserving branching bisimulation

Timed Tuplix Calculus and the Wesseling and van den Bergh Equation

Deciding orthogonal bisimulation

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