Deriving Bisimulation Congruences for Conditional Reactive Systems

Hülsbusch, Mathias; König, Barbara

doi:10.1007/978-3-642-28729-9_24

Cited by 6 publications

(15 citation statements)

References 16 publications

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“…The concept of having environmental variables to allow for different versions of a transition system can also be extended to graph transformation systems, or, more generally, reactive systems. We are currently working on conditional transition systems in the context of reactive systems, extending previous work on conditional reactive systems [39].…”

Section: Discussionmentioning

confidence: 90%

Conditional transition systems with upgrades

Beohar

König

Küpper

et al. 2020

Science of Computer Programming

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We introduce a variant of transition systems, where activation of transitions depends on conditions of the environment and upgrades during runtime potentially create additional transitions. Using a cornerstone result in lattice theory, we show that such transition systems can be modelled in two ways: as conditional transition systems (CTS) with a partial order on conditions, or as lattice transition systems (LaTS), where transitions are labelled with the elements from a distributive lattice. We define equivalent notions of bisimilarity for both variants and characterise them via a bisimulation game. We explain how conditional transition systems are related to featured transition systems for the modelling of software product lines. Furthermore, we show how to compute bisimilarity symbolically via BDDs by defining an operation on BDDs that approximates an element of a Boolean algebra into a lattice. We have implemented our procedure and provide runtime results. This is an extended version of the TASE 2017 paper [1], including all proofs, additional examples, an extension of the formalism to account for deactivation of updates and detailed runtime results.

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Section: Discussionmentioning

confidence: 90%

Conditional transition systems with upgrades

Beohar

König

Küpper

et al. 2020

Science of Computer Programming

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“…Reactive Systems without Conditions. We now define reactive systems, which were introduced in [LM00] and extended in [HK12] with application conditions for rules. We initially only look at reactive systems without conditions.…”

Section: Reactive Systemsmentioning

confidence: 99%

“…In order to obtain a congruence, we can resort to defining bisimulation on labelled transitions, using as labels the additional contexts that allow an agent to react [LM00,HK12].…”

Section: Deriving Bisimulation Congruences the Reduction Relationmentioning

confidence: 99%

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Conditional Bisimilarity for Reactive Systems

Hülsbusch¹,

König²,

Küpper³

et al. 2022

Logical Methods in Computer Science

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Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to obtain a compositional semantics. We enrich the notion of reactive systems by conditions on two levels: first, as in earlier work, we consider rules enriched with application conditions and second, we investigate the notion of conditional bisimilarity. Conditional bisimilarity allows us to say that two system states are bisimilar provided that the environment satisfies a given condition. We present several equivalent definitions of conditional bisimilarity, including one that is useful for concrete proofs and that employs an up-to-context technique, and we compare with related behavioural equivalences. We consider examples based on DPO graph rewriting, an instantiation of reactive systems.

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“…Moreover, no correctness proof is included. On the other hand, in [10], the authors extend BC-transformation to the case of conditional transformation systems. Even if their results mainly apply to the case of non-attributed graphs, their notion of context transition is, in a way, related to our symbolic transitions and so they are the corresponding notions of bisimilarity.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Checking Bisimilarity for Attributed Graph Transformation

Orejas

Boronat

Golas

et al. 2013

Lecture Notes in Computer Science

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Abstract. Borrowed context graph transformation is a technique developed byEhrig and Koenig to define bisimilarity congruences from reduction semantics defined by graph transformation. This means that, for instance, this technique can be used for defining bisimilarity congruences for process calculi whose operational semantics can be defined by graph transformation. Moreover, given a set of graph transformation rules, the technique can be used for checking bisimilarity of two given graphs. Unfortunately, we can not use this ideas to check if attributed graphs are bisimilar, i.e. graphs whose nodes or edges are labelled with values from some given data algebra and where graph transformation involves computation on that algebra. The problem is that, in the case of attributed graphs, borrowed context transformation may be infinitely branching. In this paper, based on borrowed context transformation of what we call symbolic graphs, we present a sound and relatively complete inference system for checking bisimilarity of attributed graphs. In particular, this means that, if using our inference system we are able to prove that two graphs are bisimilar then they are indeed bisimilar. Conversely, two graphs are not bisimilar if and only if we can find a proof saying so, provided that we are able to prove some formulas over the given data algebra. Moreover, since the proof system is complex to use, we also present a tableau method based on the inference system that is also sound and relatively complete.

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Deriving Bisimulation Congruences for Conditional Reactive Systems

Cited by 6 publications

References 16 publications

Conditional transition systems with upgrades

Conditional transition systems with upgrades

Conditional Bisimilarity for Reactive Systems

Checking Bisimilarity for Attributed Graph Transformation

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