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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1994: STACS 94 pp 97–108Cite as

Quasilinear time complexity theory

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 775))

Abstract

This paper furthers the study of quasi-linear time complexity initiated by Schnorr [Sch76] and Gurevich and Shelah [GS89]. We show that the fundamental properties of the polynomial-time hierarchy carry over to the quasilineartime hierarchy. Whereas all previously known versions of the Valiant-Vazirani reduction from NP to parity run in quadratic time, we give a new construction using error-correcting codes that runs in quasilinear time. We show, however, that the important equivalence between search problems and decision problems in polynomial time is unlikely to carry over: if search reduces to decision for SAT in quasi-linear time, then all of NP is contained in quasi-polynomial time. Other connections to work by Stearns and Hunt [SH86, SH90, HS90] on “power indices” of NP languages are made.

Supported in part by NSF grant CCR-9002292.

Supported in part by NSF grant CCR-9011248.

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Author information

Authors and Affiliations

  1. SUNY Buffalo, USA

    Ashish V. Naik, Kenneth W. Regan & D. Sivakumar

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  1. Ashish V. Naik
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  2. Kenneth W. Regan
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  3. D. Sivakumar
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Editor information

Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

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© 1994 Springer-Verlag Berlin Heidelberg

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Naik, A.V., Regan, K.W., Sivakumar, D. (1994). Quasilinear time complexity theory. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_134

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  • DOI: https://doi.org/10.1007/3-540-57785-8_134

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  • Print ISBN: 978-3-540-57785-0

  • Online ISBN: 978-3-540-48332-8

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