Graphes et hypergraphes : complexités algorithmique et algébrique

Abstract : Beware, this abstract comports irony and humor. In this dissertation, we defend the idea that, for any reasonnable model of computation, this is not the model that is important to caracterize important complexity classes. Instead, what matters is the complexity of the underlying combinatorial structure and, at the end, the underlying graph. If we take the example of boolean or algebraic circuits as models, all that matters is the complexity of the underlying digraph. By a reasonnable model of computation, we mean, as is requested, a model that when studied on a standard class of graphs will give the standard complexity class we expect, in order to statisfy the elementary rules of tautologies. One could also choose as reasonnable models the Turing-complete models (or another notion of completeness more suited to the computed objects), that can be formalized in a simple logic (in order to avoid "cheats" and models designed specialy to falsify this beautiful claim). Nevertheless, since this second option may be risky, we only propose it. The defended thesis is a more formalized and more mathematically precise version of this idea with hollow limits (and hence a little false as it is).
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Contributor : Laurent Lyaudet <>
Submitted on : Monday, November 18, 2013 - 7:32:52 PM
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Laurent Lyaudet. Graphes et hypergraphes : complexités algorithmique et algébrique. Complexité [cs.CC]. Ecole normale supérieure de lyon - ENS LYON, 2007. Français. ⟨tel-00905137⟩

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