Mahaney's theorem is a theorem in computational complexity theory proven by Stephen Mahaney that states that if any sparse language is NP-complete, then...

co-NP-complete, then P = NP. Mahaney used this to show in 1982 that if any sparse language is NP-complete, then P = NP (this is Mahaney's theorem). A simpler proof...

of research on the structure of NP-complete sets, culminating in Mahaney's theorem on the nonexistence of sparse NP-complete sets. He and his coauthors...

Exponential Hierarchy Jin-Yi Cai. Lecture 11: P/poly, Sparse Sets, and Mahaney's Theorem. CS 810: Introduction to Complexity Theory. The University of Wisconsin–Madison...

(or even just co-NP-hard), then P = NP, a critical foundation for Mahaney's theorem. A decision problem C is co-NP-complete if it is in co-NP and if every...

NP/poly is used in a variation of Mahaney's theorem on the non-existence of sparse NP-complete languages. Mahaney's theorem itself states that the number...

reductions) is in fact equivalent to the statement that P ≠ NP; this is Mahaney's theorem. Even for a relaxed definition of NP-completeness using Turing reductions...

[1] Lance Fortnow. Favorite Theorems: Small Sets. April 18, 2006. http://weblog.fortnow.com/2006/04/favorite-theorems-small-sets.html Complexity Zoo:...