Divide and congruence III: From decomposition of modal formulas to preservation of stability and divergence

Fokkink, Wan; Glabbeek, Rob van; Luttik, Bas

doi:10.1016/j.ic.2019.104435

“…Third, the current treatment of up-to context heavily relies on positive formats; whether our results can be extended to rule formats with negative premises is left open. Perhaps the modal decomposition approach to congruence results [7,8] can help-investigating the relation of this approach to up-to techniques is an exciting direction of research. Finally, extension of the formats to languages including a recursion construct would be very interesting, especially since the proofs that weak and branching bisimilarity are compatible with this construct use up-to techniques [14,10].…”

Section: Discussionmentioning

confidence: 99%

Up-to Techniques for Branching Bisimilarity

Erkens

¹

,

Rot

²

,

Luttik

³

2020

SOFSEM 2020: Theory and Practice of Computer Science

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Ever since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of up-to techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloom's BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also η, delay and weak bisimilarity. ⋆ The research of the second author was supported by a Marie Curie Fellowship (grant code 795119). An extended abstract has been published in the proceedings of SOF-SEM 2020, see https://doi.

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“…The operational rules presented in Fig 6 are in the so-called panth format from which it immediately follows that strong bisimilarity is a congruence [Ver95]. Due to the sequencing operator, rooted branching bisimulation is no longer a congruence, and we have to add an extra condition: rooted divergence-preserving branching bisimulation [GW96, Lut20] is a congruence, which can be proved using [FGL19].…”

Section: Sequential Processes: Tsp ;mentioning

confidence: 99%

Pushdown Automata and Context-Free Grammars in Bisimulation Semantics

Baeten¹,

Carissimo²,

Luttik³

2023

Logical Methods in Computer Science

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The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings. In the Reactive Turing Machine, transitions have labels to give a notion of interactivity. In the resulting process graph, we use bisimilarity instead of language equivalence. Subsequently, we considered other classical theorems and notions from automata theory and formal languages theory. In this paper, we consider the classical theorem of the correspondence between pushdown automata and context-free grammars. By changing the process operator of sequential composition to a sequencing operator with intermediate acceptance, we get a better correspondence in our setting. We find that the missing ingredient to recover the full correspondence is the addition of a notion of state awareness.

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“…The operational rules presented in Fig 3 are in the so-called panth format from which it immediately follows that strong bisimilarity is a congruence [Ver95]. In the case of rooted divergencepreserving branching bisimulation, we have to use [FvGL19] in order to show it is a congruence.…”

Section: Sequential Processesmentioning

confidence: 99%

Pushdown Automata and Context-Free Grammars in Bisimulation Semantics

Baeten¹,

Carissimo²,

Luttik³

2022

Preprint

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0

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The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings. In the Reactive Turing Machine, transitions have labels to give a notion of interactivity. In the resulting process graph, we use bisimilarity instead of language equivalence. Subsequently, we considered other classical theorems and notions from automata theory and formal languages theory. In this paper, we consider the classical theorem of the correspondence between pushdown automata and context-free grammars. By changing the process operator of sequential composition to a sequencing operator with intermediate acceptance, we get a better correspondence in our setting. We find that the missing ingredient to recover the full correspondence is the addition of a notion of state awareness.

show abstract

Divide and congruence III: From decomposition of modal formulas to preservation of stability and divergence

Cited by 10 publications

References 32 publications

Up-to Techniques for Branching Bisimilarity

Up-to Techniques for Branching Bisimilarity

Pushdown Automata and Context-Free Grammars in Bisimulation Semantics

Pushdown Automata and Context-Free Grammars in Bisimulation Semantics

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