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On the Automatizability of Polynomial Calculus

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Abstract

We prove that Polynomial Calculus and Polynomial Calculus with Resolution are not automatizable, unless W[P]-hard problems are fixed parameter tractable by one-side error randomized algorithms. This extends to Polynomial Calculus the analogous result obtained for Resolution by Alekhnovich and Razborov (SIAM J. Comput. 38(4):1347–1363, 2008).

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Authors and Affiliations

  1. Department of Computer Science, Sapienza—Università di Roma, Roma, Italy

    Nicola Galesi & Massimo Lauria

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  1. Nicola Galesi
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  2. Massimo Lauria
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Correspondence to Massimo Lauria.

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Research of N. Galesi was supported by La Sapienza research projects: (1) “Algoritmi efficienti su modelli avanzati di comunicazione e di calcolo” and (2) “Limiti di compressione in combinatoria e complessit computazionale”.

Research of M. Lauria was partially founded by the grant #13393 of Templeton Foundation.

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Galesi, N., Lauria, M. On the Automatizability of Polynomial Calculus. Theory Comput Syst 47, 491–506 (2010). https://doi.org/10.1007/s00224-009-9195-5

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  • DOI: https://doi.org/10.1007/s00224-009-9195-5

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