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This paper presents the classification of digital n-manifolds based on the notion of complexity and homotopy equivalence.
This function is recursively built through a stratification of the set of concepts at hand based on a notion of complexity.
Results of the simulations are compared with experimental data, and a notion of complexity is introduced to quantify the behavior of the system in different conditions.
We manage to establish a dichotomy theorem for this stronger notion of complexity: if a query is what Ron Fagin calls beta-acyclic, then Minesweeper runs in time linear in the certificate; if a query is beta-cyclic than on some instance any algorithm takes time that is super linear in the certificate.
THE 1995 Projects exhibition at the Museum of Modern Art in New York included works that he created to address this new-found notion of complexity -- notably "Everything," a 36-by-36-inch 36-by-36-inch 36-by-36-inch 36-by-36-inchword in the English dictionary, and "Loopieceof which he cooked a box of spapertti and then contocted the pieces end-to-end to form one continuous circuit.
Another notion of complexity is studied in descriptive complexity theory (e.g., Immerman 1999).
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There appears to be no current consensus on whether the sense in which these systems are regarded as 'complex' is related to any of the notions of complexity studied in computer science.
Perhaps these people will then start to appreciate some of the things that I appreciate too, the notions of complexity from simplicity, emergent behavior etc.
This, his most recent work, is a hybrid reflection surrounding notions of complexity, infinity, and chaos which will be presented for the very first time this week during the French festival EXIT.
Furthermore, despite claims to the contrary, neither William Dembski's criterion of specified complexity (Dembski 1998a) nor Michael Behe's notion of irreducible complexity (Behe 1996) provides convincing evidence of the need for an intelligent agent these ideas have not borne fruit (Wilkins and Elsberry 2001; Shanks and Joplin 1999).
However, Kolmogorov complexity does not correspond to our intuitive notion of biological complexity.
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