Abstract and concrete categories
Abstract and concrete categories
MFPS '92 Selected papers of the meeting on Mathematical foundations of programming semantics
On the greatest fixed point of a set functor
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Lifting Theorems for Kleisli Categories
Proceedings of the 9th International Conference on Mathematical Foundations of Programming Semantics
On the final sequence of a finitary set functor
Theoretical Computer Science
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Coalgebraic minimization of HD-automata for the π-calculus using polymorphic types
Theoretical Computer Science - Formal methods for components and objects
Weighted Bisimulation in Linear Algebraic Form
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
DLT'11 Proceedings of the 15th international conference on Developments in language theory
From T-coalgebras to filter structures and transition systems
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Coalgebraic trace semantics for probabilistic transition systems based on measure theory
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Algebra-coalgebra duality in brzozowski's minimization algorithm
ACM Transactions on Computational Logic (TOCL)
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Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this paper, we use the coalgebraic view on systems to derive, in a uniform way, abstract procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization. First, we show that for coalgebras in categories equipped with factorization structures, there exists an abstract procedure for equivalence checking. Then, we consider coalgebras in categories without suitable factorization structures: under certain conditions, it is possible to apply the above procedure after transforming coalgebras with reflections. This transformation can be thought of as some kind of determinization. We will apply our theory to the following examples: conditional transition systems and (non-deterministic) automata.