J.J.M.M. Rutten , "Coalgebra, Concurrency, and Control, " Research Report CWI, SEN-R9921, Amsterdam, 1999.  Home/Search   Document Details and Download   Summary   Related Articles

....1 Introduction Coalgebras are well suited for the study of automata and their various extensions, and more generally, for state transition (dynamical) systems. Discrete event systems are often represented by automata viewed as a particular algebraic structure. However, it has been shown in [5] that they can be also viewed as deterministic partial automata (automata with partial transition function) These are coalgebras of a simple functor of the category of sets. Coalgebras are categorial duals of algebras (the corresponding functor operates from a given set rather than to a given ....

..... Notice that if L a is defined, then L and L a is prefix closed. The following notational conventions will be used: L i# # Lw i# Lw is defined i# w . Denote by L the prefix closure of L, whose definition is extended to partial languages componentwise. Recall from [5] that automaton (L, L #) is final among all partial automata: for any automaton S = S, t#) there exists a unique homomorphism l : S # L. S, s s # i# l(s) l(s # ) Another characterization of finality of is that it satisfies the principle of coinduction: for all K and L in , if ....

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J.J.M.M. Rutten , "Coalgebra, Concurrency, and Control, " Research Report CWI, SEN-R9921, Amsterdam, 1999.

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