Physical Sciences and Mathematics Commons^™

The Isomorphism Conjecture Fails Relative To A Random Oracle, Stuart A. Kurtz, Stephen R. Mahaney, James S. Royer

Electrical Engineering and Computer Science - All Scholarship

Berman and Hartmanis [BH77] conjectured that there is a polynomialtime computable isomorphism between any two languages complete for NP with respect to polynomial-time computable many-one (Karp) reductions. Joseph and Young [JY85] gave a structural definition of a class of NP-complete sets---the k-creative sets---and defined a class of sets (the K k f 's) that are necessarily k-creative. They went on to conjecture that certain of these K k f 's are not isomorphic to the standard NP-complete sets. Clearly, the Berman--Hartmanis and Joseph--Young conjectures cannot both be correct. We introduce a family of strong one-way functions, the scrambling functions. If …