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The operators minCh and maxCh on the polynomial hierarchy

  • Holger Spakowski
  • Jörg Vogel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)

Abstract

In this paper we introduce a new acceptance concept for nondeterministic Turing machines with output device which allows a characterization of the complexity class Θ 2 p = PNP[log] as a polynomial time bounded class. Thereby the internal structure of the output is essential: it looks at output with maximal number of mind changes instead of output with maximal value which was realized for the first time by Krentel [Kre88].

Motivated by this characterization we define in a general way two operators, the so called maxCh- and minCh- operator, respectively which are special types of optimization operators.

Following a paper by Hempel/Wechsung [HW96] we investigate the behaviour of these operators on the polynomial hierarchy. We prove a collection of relations regarding the interaction of operators maxCh, minCh, $, Θ, Θ, Θ, Sig, C and U. So we get a tool to show that the maxCh- and minCh- classes are distinct under reasonable structural assumptions. Finally, our proof techniques allow to solve one of the open questions of Hempel/Wechsung.

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References

  1. [HW96]
    H. Hempel, G. Wechsung. The Operators and max on the Polynomial Time Hierarchy. Proceedings of STACS 97, LNCS 1200, 93–104CrossRefGoogle Scholar
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    J. Köbler, U. Schöning, J. Torán. On counting and approximation. Acta Informatica, 26 (1989), 363–379zbMATHMathSciNetGoogle Scholar
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    M. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36 (1988), 490–509zbMATHCrossRefMathSciNetGoogle Scholar
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    C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994Google Scholar
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    H. Vollmer. Komplexitätsklassen von Funktionen. PhD thesis, Universität Würzburg, Institut für Informatik, Würzburg, Germany, 1994Google Scholar
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    K.W. Wagner. Bounded query classes. SIAM Journal on Computing, 19(1990), 833–846zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Holger Spakowski
    • 1
  • Jörg Vogel
    • 2
  1. 1.Dept. of Math. and Computer ScienceErnst Moritz Arndt UniversityGreifswaldGermany
  2. 2.Computer Science InstituteFriedrich Schiller UniversityJenaGermany

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