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)


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.


Turing Machine Proof System Canonical Pair Degree Structure Disjoint Pair 
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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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