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Summary: RELATING EQUIVALENCE AND REDUCIBILITY TO SPARSE SETS
ERIC ALLENDER
DEPARTMENT OF COMPUTER SCIENCE
RUTGERS UNIVERSITY
NEW BRUNSWICK, NJ 08903
LANE A. HEMACHANDRAy
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF ROCHESTER
ROCHESTER, NY 14627
MITSUNORI OGIWARAz
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF ELECTRO-COMMUNICATIONS
TOKYO 182
OSAMU WATANABE
DEPARTMENT OF COMPUTER SCIENCE
TOKYO INSTITUTE OF TECHNOLOGY
TOKYO 152
Abstract. For various polynomial-time reducibilities r, this paper asks 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 6= NP, this
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