Relations and graphs: discrete mathematics for computer scientists
Relations and graphs: discrete mathematics for computer scientists
ACM Transactions on Computational Logic (TOCL)
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
A Relation-Algebraic Theory of Bisimulations
Fundamenta Informaticae
Circulations, Fuzzy Relations and Semirings
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Synthesis of Optimal Control Policies for Some Infinite-State Transition Systems
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Complete lattices and up-to techniques
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
On the cardinality of relations
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
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
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Equivalences, partitions and (bi)simulations are usually tackled using concrete relations. There are only few treatments by abstract relation algebra or category theory. We give an approach based on the theory of semirings and quantales. This allows applying the results directly to structures such as path and tree algebras which is not as straightforward in the other approaches mentioned. Also, the amount of higher-order formulations used is low and only a one-sorted algebra is used. This makes the theory suitable for fully automated first-order proof systems. As a small application we show how to use the algebra to construct a simple control policy for infinite-state transition systems.