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Characterizing Valiant's algebraic complexity classes

Autor: Guillaume Malod, Natacha Portier

Publikováno v: Journal of Complexity. 24:16-38

Valiant introduced 20 years ago an algebraic complexity theory to study the complexity of polynomial families. The basic computation model used is the arithmetic circuit, which makes these classes very easy to define and open to combinatorial techniq

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9dbe475c53b18a9d137aee726b46fa32
https://doi.org/10.1016/j.jco.2006.09.006

Symmetric Determinantal Representation of Formulas and Weakly Skew Circuits

Autor: Bruno Grenet, Erich Kaltofen, Pascal Koiran, Natacha Portier

Publikováno v: Randomization, Relaxation, and Complexity in Polynomial Equation Solving
Leonid Gurvits, Philippe Pebay, J. Maurice Rojas, David Thompson. Randomization, Relaxation, and Complexity in Polynomial Equation Solving, Amer. Math. Soc., pp.61-96, 2011, Contemporary Mathematics, 978-0-8218-5228-6. ⟨10.1090/conm/556⟩

We deploy algebraic complexity theoretic techniques for constructing symmetric determinantal representations of for00504925mulas and weakly skew circuits. Our representations produce matrices of much smaller dimensions than those given in the convex

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::714c37736440a0edada3b2e6da3d82ab
https://ens-lyon.hal.science/ensl-00504925v4/document

On the expressive power of permanents and perfect matchings of matrices of bounded pathwidth/cliquewidth

Autor: Uffe Flarup, Laurent Lyaudet

Publikováno v: Theory of Computing Systems
Theory of Computing Systems, Springer Verlag, 2010, 46 (4), pp.761-791. ⟨10.1007/s00224-009-9241-3⟩
Flarup, U & Lyaudet, L 2008, ' On the expressive power of permanents and perfect matchings of matrices of bounded pathwidth/cliquewidth ', Paper presented at International Computer Science Symposium in Russia, Moskva, Russian Federation, 07/06/2008-12/06/2008 .

Some 25 years ago Valiant introduced an algebraic model of computation in order to study the complexity of evaluating families of polynomials. The theory was introduced along with the complexity classes VP and VNP which are analogues of the classical

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b68e9b7107bcb0cb25c2ee4601974ebf
https://ens-lyon.hal.science/ensl-00212158

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