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Abstract: . Algebraic structures which are generated by a collection of constructors--- like natural numbers (generated by a zero and a successor) or finite lists and trees--- are of well-established importance in computer science. Formally, they are initial algebras. Induction is used both as a definition principle, and as a proof principle for such structures. But there are also important dual "coalgebraic" structures, which do not come equipped with constructor operations but with what are sometimes... (Update)
Context of citations to this paper: More
.... is based on coinductive principles [BM] which are more expressive than the inductive principles underlying Turing computable functions [JR,WG2]. As a result, OE M cannot be expressed by any Turing computable function. Theorem 6.1. For any PTMs M 1 and M 2 , L(M 1 ) L(M 2 )...
.... is based on coinductive principles [BM] which are more expressive than the inductive principles underlying Turing computable functions [JR, WG]. Though frec returns the output stream properly, it represents the state explicitly among its inputs, so it is not quite what we...
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BibTeX entry: (Update)
Bart Jacobs, Jan Rutten. A Tutorial on Coalgebras and Coinduction. EATCS Bulletin 62 (1997), pp. 222-259. http://citeseer.ist.psu.edu/jacobs97tutorial.html More
@article{ jacobs97tutorial,
author = "Bart Jacobs and Jan Rutten",
title = "A Tutorial on (Co)Algebras and (Co)Induction",
journal = "Bulletin of the European Association for Theoretical Computer Science",
volume = "62",
pages = "222--259",
year = "1997",
url = "citeseer.ist.psu.edu/jacobs97tutorial.html" }
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Documents on the same site (http://www.cwi.nl/~bjacobs/papers.html): More
Mongruences and Cofree Coalgebras - Jacobs (1995) (Correct)
Object-Oriented Hybrid Systems of Coalgebras plus Monoid Actions - Bart Jacobs (1996) (Correct)
An Algebraic View of Structural Induction - Hermida, Jacobs (1994) (Correct)
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