One-Way Functions and the Berman-Hartmanis Conjecture

—The Berman-Hartmanis conjecture states that all NP-complete sets are P-isomorphic each other. On this conjecture, we first improve the result of [3] and show that all NP-complete sets are ≤ p/poly li,1-1 -reducible to each other based on the assumption that there exist regular one-way functions that cannot be inverted by randomized polynomial-time algorithms. Secondly, we show that, besides the above assumption, if all one-way functions have some easy part to invert, then all NP-complete sets are P/polyisomorphic to each other.

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: Manindra Agrawal, Osamu Watanabe
• Keywords: Berman-Hartmanis Conjecture States, COCO 2009, NP-complete Sets, One-way Functions, Theoretical Computer Science