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More complicated questions about maxima and minima, and some closures of NP

  • Klaus W. Wagner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)

Abstract

Starting from NP-complete problems defined by questions of the kind "max ... ≥ k?" and "min ... ≤ k?" we consider problems defined by more complicated questions about these maxima and minima, as for example "max ... = k?", "min ... ε M?" and "is max ... odd?". This continues a work started by Papadimitriou and Yannakakis in [PaYa 82]. It is shown that these and other problems are complete in certain subclasses of the Boolean closure of NP and other classes in the interesting area below the class Δ 2 P of the polynomial-time hierarchie. Special methods are developped to prove such completeness results. For this it is necessary to establish some properties of the classes in question which might be interesting in their own right.

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6. References

  1. [GaJo 79]
    Garey, M.R., Johnson, D.S., Computers and Intractibility: A Guide to the Theory of NP-Completeness, Freeman, San Francisco 1979Google Scholar
  2. [Hau 14]
    Hausdorff, F., Grundzüge der Mengenlehre, Leipzig 1914Google Scholar
  3. [Joh 85]
    Johnson, D.S., The NP-completeness column: an ongoing guide 15th edition, Journal of Algorithms 6(1985), 291–305Google Scholar
  4. [KöSc 85]
    Köbler, J., Schöning, U., The difference and truth-table hierarchies for NP, manuscript 1985Google Scholar
  5. [LaLy 76]
    Ladner, R.E., Lynch, N.A., Relativizations of questions about log space computability, MST 10(1976), 19–32Google Scholar
  6. [LaLySe 75]
    Ladner, R.E., Lynch, N.A., Selman, A.L., A comparison of polynomial time reducibilities, TCS 1(1975), 103–123Google Scholar
  7. [Pap 84]
    Papadimitriou, C.H., On the complexity of unique solutions, JACM 31(1984), 392–400Google Scholar
  8. [PaYa 82]
    Papadimitriou, C.H., Yannakakis, M., The complexity of facets (and some facets of complexity), 14th STOC (1982), 255–260, see also: JCSS 28(1984), 244–259Google Scholar
  9. [StMe 73]
    Stockmeyer, L.J., Meyer, A.R., Word problems requiring exponential time, 5th STOC (1973), 1–9Google Scholar
  10. [Sto 77]
    Stockmeyer, L.J., The polynomial-time hierarchy, TSC 3(1977), 1–22Google Scholar
  11. [Wag 79]
    Wagner, K., On ω-regular sets, Inf.&Contr. 43(1979), 123–177Google Scholar
  12. [Wag 84a]
    Wagner, K., Compact descriptions and the counting polynomial-time hierarchy, Proc. 2nd Frege Conf. (1984), 383–392Google Scholar
  13. [Wag 84b]
    Wagner, K., The complexity of graphs with regularities, Proc. 11th MFCS Conf., LNCS 176 (1984), 544–552Google Scholar
  14. [We 85]
    Wechsung G., On the Boolean closure of NP, Proc. FCT Conf. 1985, LNCS 199 (1985), 485–493Google Scholar
  15. [WeWa 85]
    Wechsung, G., Wagner, K.W., On the Boolean closure of NP, submitted for publication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Klaus W. Wagner
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität PassauPassau

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