On One-One Polynomial Time Equivalence Relations

Abstract Two sets A and B are one-one polynomial time equivalent (one-one p-equivalent) if there are polynomial time one-one reductions from A to B and from B to A . In this paper we show that all EXPTIME complete sets are one-one p-equivalent by length increasing reductions. Moreover we show this result for many complexity classes which can be proved by a straightforward diagonalization to contain P properly. We also obtain some nontrivial examples in EXPTIME-P which show the difference between one-one and many-one polynomial time equivalence relations.