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International Colloquium on Automata, Languages, and Programming

ICALP 1992: Automata, Languages and Programming pp 162–173Cite as

Reductions to sets of low information content

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 623))

Abstract

In this paper we study the complexity of sets that reduce to sparse sets (and tally sets), and the complexity of the simplest sparse sets to which such sets reduce. We show even with respect to very flexible reductions that NP cannot have sparse hard sets unless P = NP; an immediate consequence of our results is: If any NP-complete set conjunctively reduces to a sparse set, then P = NP. We also show that any set A that reduces to some sparse set (via various types of reductions) in fact reduces by the same type of reduction to a sparse set that is simple relative to A. We give a complete characterization of the sets of low instance complexity in terms of reductions to tally sets; it follows that if P ≠ NP, then no set of low instance complexity can be complete for NP with respect to disjunctive reductions or conjunctive reductions.

Work done while visiting Universität Ulm. Supported in part by an Alexander von Humboldt postdoctoral research fellowship.

Supported in part by the National Science Foundation under research grant CCR-8957604.

Supported in part by the DAAD through Acciones Integradas 1991, 313-AI-e-es/zk.

Work supported in part by ESPRIT-II Basic Research Actions Program of the EC under Contract No. 3075 (project ALCOM) and by the DAAD through Acciones Integradas 1991, 313-AI-e-es/zk.

Work done in part while visiting SUNY-Buffalo. Supported in part by the National Science Foundation under research grant CCR-9002292.

Work done in part while visiting the University of Rochester. Supported in part by Ministero della Pubblica Istruzione through “Progetto 40%: Algoritmi. Modelli di Calcolo e Strutture Informative.”

Work done in part while visiting the University of Rochester. Supported in part by a DFG Post-doctoral Stipend and by the DAAD through Acciones Integradas 1991, 313-AI-e-es/zk.

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Author information

Authors and Affiliations

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

    V. Arvind

  2. Department of Computer Science, University of Rochester, 14627, Rochester, NY, USA

    Y. Han & L. Hemachandra

  3. Abteilung für Theoretische Informatik, Universität Ulm, D-W-7900, Oberer Eselsberg, Ulm, Germany

    J. Köbler, M. Mundhenk, U. Schöning & T. Thierauf

  4. Department of Software (L.S.I.), Universität Politècnica de Catalunya, Pau Gargallo 5, E-08028, Barcelona, Spain

    A. Lozano

  5. Department of Computer Science and Information Mathematics, University of Electro-Communications, 1-5-1, Chofugaoka, Chofu-si, 182, Tokyo, Japan

    M. Ogiwara

  6. Dipartimento Di Matematica, Universitá degli Studi di Roma, “La Sapienza”, 00198, Rome, Italy

    R. Silvestri

Authors
  1. V. Arvind
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  2. Y. Han
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  3. L. Hemachandra
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  4. J. Köbler
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  5. A. Lozano
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  6. M. Mundhenk
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  7. M. Ogiwara
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  8. U. Schöning
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W. Kuich

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© 1992 Springer-Verlag Berlin Heidelberg

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Arvind, V. et al. (1992). Reductions to sets of low information content. In: Kuich, W. (eds) Automata, Languages and Programming. ICALP 1992. Lecture Notes in Computer Science, vol 623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55719-9_72

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  • DOI: https://doi.org/10.1007/3-540-55719-9_72

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55719-7

  • Online ISBN: 978-3-540-47278-0

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