Undecidability and Definability for Parametrized Polynomial Time m-Reducibilities

  • Peter Cholak
  • Rod Downey
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 12)


In the setting of the parametrized reducibilities introduced by the second author and Mike Fellows, we prove a number of decidability and definability results. In particular the undecidability of the relevant m-degree structures is proven. The relationship with classical notions is analyzed, and this leads to a number of observations about classical constructions in the PTIME degrees. Methods include 0″, 0″′ and 0 (4) priority arguments combined with speedup type arguments.


Vertex Cover Minimal Pair Polynomial Time Reducibility Recursively Enumerable Priority Argument 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Peter Cholak
    • 1
  • Rod Downey
    • 1
    • 2
  1. 1.Mathematics DepartmentVictoria UniversityWellingtonNew Zealand
  2. 2.Mathematics Department and Mathematical Sciences InstituteCornell UniversityIthacaUSA

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