Alternating automata on infinite trees
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Extensive Games as Process Models
Journal of Logic, Language and Information
Automata and Fixed Point Logics for Coalgebras
Electronic Notes in Theoretical Computer Science (ENTCS)
Automata and fixed point logic: A coalgebraic perspective
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
On monotone modalities and adjointness
Mathematical Structures in Computer Science
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Coalgebra automata, introduced by the second author, generalize the well-known automata that operate on infinite words/streams, trees, graphs or transition systems. This coalgebraic perspective on automata lays foundation to a universal theory of automata operating on infinite models of computation. In this paper we prove a complementation lemma for coalgebra automata. More specifically, we provide a construction that transforms a given coalgebra automaton with parity acceptance condition into a device of similar type, which accepts exactly those pointed coalgebras that are rejected by the original automaton. Our construction works for automata operating on coalgebras for an arbitrary standard set functor which preserves weak pullbacks and restricts to finite sets. Our proof is coalgebraic in flavour in that we introduce and use a notion of game bisimilarity between certain kinds of parity games.