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Canonical Disjoint NP-Pairs of Propositional Proof Systems

  • Christian Glaßer
  • Alan L. Selman
  • Liyu Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)

Abstract

We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is identical. Secondly, we show that this degree structure is not superficial: Assuming there exist P-inseparable disjoint pairs, there exist intermediate disjoint NP-pairs. That is, if (A, B) is a P-separable disjoint NP-pair and (C, D) is a P-inseparable disjoint NP-pair, then there exist P-inseparable, incomparable NP-pairs (E, F) and (G, H) whose degrees lie strictly between (A, B) and (C, D). Furthermore, between any two disjoint NP-pairs that are comparable and inequivalent, such a diamond exists.

Keywords

Turing Machine Proof System Canonical Pair Degree Structure Disjoint Pair 
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 2005

Authors and Affiliations

  • Christian Glaßer
    • 1
  • Alan L. Selman
    • 2
  • Liyu Zhang
    • 2
  1. 1.Lehrstuhl für Informatik IVUniversität WürzburgWürzburgGermany
  2. 2.Department of Computer Science and EngineeringUniversity at BuffaloBuffaloUSA

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