Three partition refinement algorithms
SIAM Journal on Computing
Introduction to numerical linear algebra and optimisation
Introduction to numerical linear algebra and optimisation
Relations and graphs: discrete mathematics for computer scientists
Relations and graphs: discrete mathematics for computer scientists
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
A Relation-Algebraic Theory of Bisimulations
Fundamenta Informaticae
Model refinement using bisimulation quotients
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
Using bisimulations for optimality problems in model refinement
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Pathfinding through congruences
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
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Dioid based model refinement is an abstract framework for optimality problems on labelled graphs such as the shortest path problem or the maximum capacity problem. Here we show two facts in this area: first, via a language theoretic approach that models with a binary set of edge labels are refinable, and second, the compatibility of linear fixpoint equations with bisimulations. These equations can be used in an algebraic setting for a certain class of optimality problems. Since bisimulations can simplify the complexity of models, they can also reduce the complexity of certain optimality problems.