On hiding information form an oracle
Journal of Computer and System Sciences
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Coherent functions and program checkers
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Introduction to the theory of complexity
Introduction to the theory of complexity
On being incoherent without being very hard
Computational Complexity
P-selective self-reducible sets: a new characterization of P
Journal of Computer and System Sciences
New Collapse Consequences of NP Having Small Circuits
SIAM Journal on Computing
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
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Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question—whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all PSPACE-complete languages are polynomial-time length-decreasing self-reducible.