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On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2136)

Abstract

Several models of NP-completeness in an algebraic framework of computation have been proposed in the past, each of them hinging on a fundamental hypothesis of type P≠NP. We first survey some known implications between such hypotheses and then describe attempts to establish further connections. This leads us to the problem of relating the complexity of computational and decisional tasks and naturally raises the question about the connection of the complexity of a polynomial with those of its factors. After reviewing what is known with this respect, we discuss a new result involving a concept of approximative complexity.

Keywords

Arithmetic Operation Algebraic Model Irreducible Factor Zariski Topology Cycle Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  1. 1.Dept. of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany

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