Another Basis for the W-Hierarchy and the Tradeoff Theorem

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


We give a uniform circuit basis for the W-hierarchy. We introduce the syntactic classes G[t] and prove the Replacement and Tradeoff Theorems. These lead to evidence that the W-hierarchy is proper and give a different perspective on its naturality.


Vertex Cover Existential Quantification Programmable Logic Array Existential Formula Present Chapter 
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.


  1. 84.
    H. Bodlaender, R. Downey, M. Fellows, T. Wareham, The parameterized complexity of sequence alignment and consensus. Theor. Comput. Sci. 147(1–2), 31–54 (1994) MathSciNetGoogle Scholar
  2. 106.
    R. Boppana, M. Sipser, The complexity of finite functions, in Handbook of Theoretical Computer Science, vol. A, ed. by J. van Leeuwen (MIT Press, Cambridge, 1990), pp. 757–804 Google Scholar
  3. 243.
    R. Downey, M. Fellows, Fixed-parameter tractability and completeness. I. Basic results. SIAM J. Comput. 24(4), 873–921 (1995) MathSciNetCrossRefzbMATHGoogle Scholar
  4. 256.
    R. Downey, M. Fellows, K. Regan, Parameterized circuit complexity and the W hierarchy. Theor. Comput. Sci. 191(1–2), 97–115 (1998) MathSciNetCrossRefzbMATHGoogle Scholar
  5. 557.
    A. Paz, S. Moran, Nondeterministic polynomial optimization problems and their approximations. Theor. Comput. Sci. 15, 251–277 (1981) MathSciNetCrossRefzbMATHGoogle Scholar
  6. 620.
    M. Sipser, A complexity theoretic approach to randomness, in Proceedings of 15th ACM Symposium on Theory of Computing (STOC ’83), Boston, Massachusetts, USA, May 25–May 27, 1983, ed. by D. Johnson, et al. (ACM, New York, 1983), pp. 330–335 Google Scholar

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

Personalised recommendations