Algebraic approaches to program semantics
Algebraic approaches to program semantics
Handbook of formal languages, vol. 1
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata and Coinduction (An Exercise in Coalgebra)
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
On the Duality between Observability and Reachability
FoSSaCS '01 Proceedings of the 4th International Conference on Foundations of Software Science and Computation Structures
On Specification Logics for Algebra-Coalgebra Structures: Reconciling Reachability and Observability
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Duality and Equational Theory of Regular Languages
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
On the relevance of abstract algebra to control theory
Automatica (Journal of IFAC)
Brzozowski's algorithm (co)algebraically
Logic and Program Semantics
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Because of the isomorphism (XxA)-X@?X-(A-X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebra-coalgebra duality goes back to Arbib and Manes, who formulated it as a duality between reachability and observability, and is ultimately based on Kalman@?s duality in systems theory between controllability and observability. Recently, it was used to give a new proof of Brzozowski@?s minimization algorithm for deterministic automata. Here we will use the algebra-coalgebra duality of automata as a common perspective for the study of both varieties and covarieties, which are classes of automata and languages defined by equations and coequations, respectively. We make a first connection with Eilenberg@?s definition of varieties of languages, which is based on the classical, algebraic notion of varieties of (transition) monoids.