Coalgebraic Simulations and Congruences

Abstract : In a recent article Gorín and Schröder study λ -simulations of coalgebras and relate them to preservation of positive formulae. Their main results assume that λ is a set of monotonic predicate liftings and their proofs are set-theoretical. We give a different definition of simulation, called strong simulation, which has several advantages: Our notion agrees with that of in the presence of monotonicity, but it has the advantage, that it allows diagrammatic reasoning, so several results from the mentioned paper can be obtained by simple diagram chases. We clarify the role of λ-monotonicity by showing the equivalence of
- λ is monotonic
- every simulation is strong
- every bisimulation is a (strong) simulation
- every F-congruence is a (strong) simulation.
We relate the notion to bisimulations and F-congruences - which are defined as pullbacks of homomorphisms. We show that
- if λ is a separating set, then each difunctional strong simulation is an F -congruence,
- if λ is monotonic, then the converse is true: if each difunctional strong simulation is an F -congruence, then λ is separating.
Document type :
Conference papers
Complete list of metadatas

Cited literature [13 references]  Display  Hide  Download

https://hal.inria.fr/hal-01408755
Contributor : Hal Ifip <>
Submitted on : Monday, December 5, 2016 - 1:24:43 PM
Last modification on : Monday, December 5, 2016 - 2:56:24 PM
Long-term archiving on : Monday, March 20, 2017 - 7:49:28 PM

File

328263_1_En_7_Chapter.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

Citation

H. Gumm, Mehdi Zarrad. Coalgebraic Simulations and Congruences. 12th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2014, Grenoble, France. pp.118-134, ⟨10.1007/978-3-662-44124-4_7⟩. ⟨hal-01408755⟩

Share

Metrics

Record views

54

Files downloads

91