منابع مشابه
The continuum as a final coalgebra
We de ne the continuum up to order isomorphism, and hence up to homeomorphism via the order topology, in terms of the nal coalgebra of either the functor N×X , product with the set of natural numbers, or the functor 1+N×X . This makes an attractive analogy with the de nition of N itself as the initial algebra of the functor 1+X , disjoint union with a singleton. We similarly specify Baire space...
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This paper presents an elementary and self-contained proof of an existence theorem of nal coalgebras for endofunctors on the category of sets and functions.
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We study k-regular sequences from a coalgebraic perspective. Building on the observation that the set of streams over a semiring S can be turned into a final coalgebra, we obtain characterizations of kregular sequences in terms of finite weighted automata, finite systems of behavioral differential equations, and recognizable power series. The latter characterization is obtained via an isomorphi...
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Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences form a particularly interesting class of streams that live in both worlds at the same time: they are defined in terms of finite automata, which are basic computational structures in computer science; and they appear in mathematics in many different ways, for instance in number theory. Examples of a...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2002
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(01)00022-6