The Basic Class W[1] and an Analog of Cook’s Theorem

  • Rodney G. Downey
  • Michael R. Fellows
Part of the Texts in Computer Science book series (TCS)


We introduce the basic class W[1] and prove the fundamental analogue of the Cook–Levin Theorem. This is central to much of the hardness theory for parameterized complexity.


Turing Machine Vertex Cover Parameterized Problem Conjunctive Normal Form Satisfying Assignment 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rodney G. Downey
    • 1
  • Michael R. Fellows
    • 2
  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria UniversityWellingtonNew Zealand
  2. 2.School of Engineering and Information TechnologyCharles Darwin UniversityDarwinAustralia

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