TY - GEN

T1 - Relating equivalence and reducibility to sparse sets

AU - Allender, Eric

AU - Hemachandra, Lane A.

AU - Ogiwara, Mitsunori

AU - Watanabe, Osamu

PY - 1991/12/1

Y1 - 1991/12/1

N2 - For various polynomial-time reducibilities r, the authors ask whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P ≠ NP, the authors show that for k-truth-table reductions, k ≥ 2, equivalence and reducibility to sparse sets provably differ. Though R. Gavaldaand D. Watanabe have shown that, for any polynomial-time computable unbounded function f(·), some sets f(n)-truth-table reducible to sparse sets are not even Turing equivalent to sparse sets, the authors show that extending their result to the 2-truth-table case would provide a proof that P ≠ NP. Additionally, the authors study the relative power of different notions of reducibility and show that disjunctive and conjunctive truth-table reductions to sparse sets are surprisingly powerful, refuting a conjecture of K. Ko (1989).

AB - For various polynomial-time reducibilities r, the authors ask whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P ≠ NP, the authors show that for k-truth-table reductions, k ≥ 2, equivalence and reducibility to sparse sets provably differ. Though R. Gavaldaand D. Watanabe have shown that, for any polynomial-time computable unbounded function f(·), some sets f(n)-truth-table reducible to sparse sets are not even Turing equivalent to sparse sets, the authors show that extending their result to the 2-truth-table case would provide a proof that P ≠ NP. Additionally, the authors study the relative power of different notions of reducibility and show that disjunctive and conjunctive truth-table reductions to sparse sets are surprisingly powerful, refuting a conjecture of K. Ko (1989).

UR - http://www.scopus.com/inward/record.url?scp=0026398366&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026398366&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026398366

SN - 0818622555

SN - 9780818622557

T3 - Proceedings of the Sixth Annual Structure in Complexity Theory Conference

SP - 220

EP - 229

BT - Proc 6 Annu Struct Complexity Theor

PB - Publ by IEEE

T2 - Proceedings of the 6th Annual Structure in Complexity Theory Conference

Y2 - 30 June 1991 through 3 July 1991

ER -