A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
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Theoretical Computer Science
Direct and dual laws for automata with multiplicities
Theoretical Computer Science
Automata and Algebras in Categories
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Bisimulation relations for weighted automata
Theoretical Computer Science
Automatic proof generation in Kleene algebra
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
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A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". In this paper, we apply the defining diagrams of algebras, coalgebras, and bialgebras to categories of semimodules and semimodule homomorphisms over a commutative semiring. We then show that formal language theory and the theory of bialgebras have essentially undergone "convergent evolution". For example, formal languages correspond to elements of dual algebras of coalgebras, automata are "pointed representation objects" of algebras, automaton morphisms are instances of linear intertwiners, and a construction from the theory of bialgebras shows how to run two automata in parallel. We also show how to associate an automaton with an arbitrary algebra, which in the classical case yields the automaton whose states are formal languages and whose transitions are given by language differentiation.