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Θ supin2 -Completeness: A Classical Approach for New Results

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FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1974))

Abstract

In this paper we present an approach for proving Θp supin2 -completeness. There are several papers in which different problems of logic, of combinatorics, and of approximation are stated to be complete for parallel access to NP, i.e.Θp supin2 -complete.

There is a special acceptance concept for nondeterministic Turing machines which allows a characterization of Θp supin2 as a polynomial-time bounded class.

This characterization is the starting point of this paper. It makes a master reduction from that type of Turing machines to suitable boolean formula problems possible. From the reductions we deduce a couple of conditions that are sufficient for proving Θp supin2 -hardness. These new conditions are applicable in a canonical way. Thus we are able to do the following: (i) we can prove the Θp supin2 for different combinatorial problems (e.g. max-card-clique compare) as well as for optimization problems (e.g. the Kemeny voting scheme), (ii) we can simplify known proofs for Θp supin2 (e.g. for the Dodgson voting scheme), and (iii) we can transfer this technique for proving Δp supin2 -completeness (e.g. TSPcompare).

Supported in part by grant NSF-INT-9815095/DAAD-315-PPP-gü-ab.

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Author information

Authors and Affiliations

  1. Dept. of Math. and Computer Science, Ernst Moritz Arndt University, D-17487, GREIFSWALD, Germany

    Holger Spakowski

  2. Friedrich Schiller University Computer Science Institute, D-07740, JENA, Germany

    Jörg Vogel

Authors
  1. Holger Spakowski
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  2. Jörg Vogel
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, Hauz Khas, 110016, New Delhi, India

    Sanjiv Kapoor  & Sanjiva Prasad  & 

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Spakowski, H., Vogel, J. (2000). Θ supin2 -Completeness: A Classical Approach for New Results. In: Kapoor, S., Prasad, S. (eds) FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2000. Lecture Notes in Computer Science, vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44450-5_28

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  • DOI: https://doi.org/10.1007/3-540-44450-5_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41413-1

  • Online ISBN: 978-3-540-44450-3

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