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A coinductive calculus of streams
, 2005
"... We develop a coinductive calculus of streams based on the presence of a final coalgebra structure on the set of streams (infinite sequences of real numbers). The main ingredient is the notion of stream derivative, which can be used to formulate both coinductive proofs and definitions. In close analo ..."
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Cited by 28 (10 self)
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We develop a coinductive calculus of streams based on the presence of a final coalgebra structure on the set of streams (infinite sequences of real numbers). The main ingredient is the notion of stream derivative, which can be used to formulate both coinductive proofs and definitions. In close analogy to classical analysis, the latter are presented as behavioural differential equations. A number of applications of the calculus are presented, including difference equations, analytical differential equations, continued fractions, and some problems from discrete mathematics and combinatorics.
Elements of stream calculus
 In MFPS 2001, ENTCS 45
, 2001
"... CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ..."
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Cited by 1 (1 self)
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CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.
A final coalgebra for kregular sequences
 Horizons of the Mind: A Tribute to Prakash Panangaden, volume 8464 of Lecture Notes in Computer Science
, 2014
"... Abstract. We study kregular 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 dif ..."
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Abstract. We study kregular 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 isomorphism of final coalgebras based on the kadic numeration system. Dedication It is our greatest pleasure to dedicate this article to Prakash Panangaden on the occasion of his 60th birthday. There are not many subjects in our own research that have not been influenced by his work and ideas. Before the notion of finality in semantics became prominent in the early nineties of the previous century, Prakash was already writing [14] about infinite objects requiring “... a limit construction and a final object... ”. Another early reference that is of direct relevance for the present paper is [16], published as a report in 1985, in which streams and stream functions play a key role. For these and many other similar such inspiring examples, we are immensely grateful. 1