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Title: A Note on the Sparse Complete Sets
Authors: Fortune, Steven
Keywords: computer science
technical report
Issue Date: Oct-1978
Publisher: Cornell University
Abstract: Hartmanis and Berman have conjectured that all NP-complete sets are polynomial time isomorphic. A consequence of the conjecture is that there are no sparse NP-complete sets. We show that the existence of an NP-complete set whose complement is sparse implies P = NP. We also show that if there is a polynomial time reduction with sparse range to a PTAPE-complete set, then P=PTAPE. Keywords: reduction, polynomial time, nondeterministic polynomial time, complete sets, sparsity.
Appears in Collections:Computer Science Technical Reports

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