E. Poll and J. Zwanenburg. From algebras and coalgebras to dialgebras. In A. Corradini, M. Lenisa, and U. Montanari, editors, Coalgebraic Methods in Computer Science '01, volume 44 of ENTCS. Elsevier, Amsterdam, 2001. Home/Search Document Details and Download
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Greatest Bisimulations for Binary Methods - Tews (2002) (1 citation) (Correct)
....are functional bisimulations, and many other standard results (again, I refer to [14] An important question left open in [14] is under which conditions bisimilarity as greatest bisimulation does exists for generalised coalgebras. This omission stimulated the interest of Poll and Zwanenburg. In [10] they show that for their notion of dialgebra a greatest bisimulation does always exists. The result of Poll and Zwanenburg implies that for some coalgebras of (proper) extended polynomial functors a greatest bisimulation does exist. This in turn spurred me on, and based on ideas drawn from [10] ....
....In [10] they show that for their notion of dialgebra a greatest bisimulation does always exists. The result of Poll and Zwanenburg implies that for some coalgebras of (proper) extended polynomial functors a greatest bisimulation does exist. This in turn spurred me on, and based on ideas drawn from [10] the present paper makes the following contributions: Section 4 generalises the cited result of Poll and Zwanenburg slightly and adopts it to the framework of [14] The main result in Section 4 is Theorem 4.6. It says that for extended cartesian functors (a proper subclass of extended polynomial ....
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E. Poll and J. Zwanenburg. From algebras and coalgebras to dialgebras. In A. Corradini, M. Lenisa, and U. Montanari, editors, Coalgebraic Methods in Computer Science '01, volume 44 of ENTCS. Elsevier, Amsterdam, 2001.
Coalgebras For Binary Methods: Properties Of Bisimulations And.. - Tews (2001) (2 citations) (Correct)
....intuitively any state of a system is behavioral equivalent with itself, so any sensible bisimulation should contain the equality relation and thus be partially reflexive. The last proposition implies that there is an upper bound for every two bisimulations that contain the equality relation. In [20] Poll and Zwanenburg prove that for dialgebras bisimulation equivalences (i.e. bisimulations that are equivalence relations) form a complete lattice. This result can be slightly generalized to a proper subclass of extended polynomial functors. Details will appear elsewhere. One direction for ....
....functors has further the advantage that binary methods can be specified within the coalgebraic framework. There are many directions for further research: One interesting point is, whether it is possible to derive more results about the union of bisimulations. The result of Poll and Zwanenburg in [20] on the union of bisimulation equivalences in the context of dialgebras can be slightly generalised to a subclass of extended polynomial functors. It is an open question if one can give a sufficient condition for coalgebras of extended polynomial functors that implies a complete lattice of ....
E. Poll and J. Zwanenburg. From algebras and coalgebras to dialgebras. In A. Corradini, M. Lenisa, and U. Montanari, editors, Coalgebraic Methods in Computer Science '01, volume 44 of ENTCS. Elsevier, Amsterdam, 2001.
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