%0 Conference Proceedings
%T Coalgebraic Simulations and Congruences
%+ Philipps Universität Marburg = Philipps University of Marburg
%A Gumm, H., Peter
%A Zarrad, Mehdi
%Z Part 2: Regular Contributions
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 12th International Workshop on Coalgebraic Methods in Computer Science (CMCS)
%C Grenoble, France
%Y Marcello M. Bonsangue
%3 Coalgebraic Methods in Computer Science
%V LNCS-8446
%P 118-134
%8 2014-04-05
%D 2014
%R 10.1007/978-3-662-44124-4_7
%Z Computer Science [cs]Conference papers
%X In a recent article Gorín and Schröder study <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>&#x03BB;<!-- λ --></mi> </math>-simulations of coalgebras and relate them to preservation of positive formulae. Their main results assume that <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>&#x03BB;<!-- λ --></mi> </math> 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 <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>&#x03BB;<!-- λ --></mi></math>-monotonicity by showing the equivalence of<br>- <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>&#x03BB;<!-- λ --></mi> </math> is monotonic<br>- every simulation is strong<br>- every bisimulation is a (strong) simulation<br>- every F-congruence is a (strong) simulation.<br>We relate the notion to bisimulations and F-congruences - which are defined as pullbacks of homomorphisms. We show that<br>- if <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>&#x03BB;<!-- λ --></mi> </math> is a separating set, then each difunctional strong simulation is an <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>F</mi> </math>-congruence,<br>- if <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>&#x03BB;<!-- λ --></mi> </math> is monotonic, then the converse is true: if each difunctional strong simulation is an <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>F</mi> </math>-congruence, then <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>&#x03BB;<!-- λ --></mi> </math> is separating.
%G English
%Z TC 1
%Z WG 1.3
%2 https://inria.hal.science/hal-01408755/document
%2 https://inria.hal.science/hal-01408755/file/328263_1_En_7_Chapter.pdf
%L hal-01408755
%U https://inria.hal.science/hal-01408755
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-LNCS-8446
%~ IFIP-WG1-3
%~ IFIP-CMCS