It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of so-called silent actions is not yet fully developed. In this paper, we give a coalgebraic characterisation of branching (delay) bisimulation in the context of labelled transition systems (fully probabilistic systems). It is shown that recording executions (up to a notion of stuttering), rather than the set of successor states, from a state is sufficient to characterise the respected bisimulation relations in both cases.
@InProceedings{beohar_et_al:LIPIcs.CALCO.2017.6, author = {Beohar, Harsh and K\"{u}pper, Sebastian}, title = {{On Path-Based Coalgebras and Weak Notions of Bisimulation}}, booktitle = {7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)}, pages = {6:1--6:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-033-0}, ISSN = {1868-8969}, year = {2017}, volume = {72}, editor = {Bonchi, Filippo and K\"{o}nig, Barbara}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2017.6}, URN = {urn:nbn:de:0030-drops-80362}, doi = {10.4230/LIPIcs.CALCO.2017.6}, annote = {Keywords: Paths, Executions, Branching bisimulation, Coalgebras} }
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