TY - GEN

T1 - Reductions to sets of low information content

AU - Arvind, V.

AU - Han, Y.

AU - Hemachandra, L.

AU - Köbler, J.

AU - Lozano, A.

AU - Mundhenk, M.

AU - Ogiwara, M.

AU - Schöning, U.

AU - Silvestri, R.

AU - Thierauf, T.

N1 - Funding Information:
*Department of Computer Science and Engineering, Indian Institute of Technology, DeLhi, New Delhi 110016, India. Work done while visiting Unlversit~/t Ulm. Supported in part by an Alexander von Humboldt postdoctoral research fellowship.
Funding Information:
IDepartment of Computer Science, University of Rochester, Rochester, NY 14627, USA. Supported in part by the National Science Foundation under research grant CCR-8957604. t Abteilung ffir Theoretische Informatik, Universit/~t Uhn, Oberer Eselsberg~ D-W-7900 Uhn, Germany. Supported in part by the DAAD through Acciones Integradas 1991, 313-AI-e-es/zk. w of Software (L.S.I.), Universitat Polit~cnica de Catalunya, Pau Gargallo 5, E-08028 Barcelona, Spain. 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 Aceiones Integradas 1991, 313-AI-e-es/zk. 82 of Computer Science and Information Mathematics, University of Electro-Commmfications, 1-5-1, Chofngaoka, Chofu-si, Tokyo 182, Japan. Work done in part while visiting SUNY-Buffalo. Supported in part by the National Science Foundation under research grant CCR-9002292. //Dipartimento Di Matematica, Unlversits degli Studi di Roma, "La Sapienza," 00198 Rome, Italy. 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." **Abteilung ffir Theoretische Informatik, Universit~t Uhn, Oberer Eselsberg, D-W-7900 Ulm, Germany. 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.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

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U2 - 10.1007/3-540-55719-9_72

DO - 10.1007/3-540-55719-9_72

M3 - Conference contribution

AN - SCOPUS:84976776860

SN - 9783540557197

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 162

EP - 173

BT - Automata, Languages and Programming - 19th International Colloquium, Proceedings

A2 - Kuich, Werner

PB - Springer Verlag

T2 - 19th International Colloquium on Automata, Languages, and Programming, ICALP 1992

Y2 - 13 July 1992 through 17 July 1992

ER -