Autoreducibility of Random Sets: A Sharp Bound on the Density of Guessed Bits
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Autoreducibility, mitoticity, and immunity
Journal of Computer and System Sciences
Pseudorandomness and Average-Case Complexity Via Uniform Reductions
Computational Complexity
SIGACT news complexity theory column 64
ACM SIGACT News
Randomness and completeness in computational complexity
Randomness and completeness in computational complexity
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Mitosis in computational complexity
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Autoreducibility, mitoticity, and immunity
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Autoreducibility of complete sets for log-space and polynomial-time reductions
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
| Hi-index | 0.00 |
A set is autoreducible if it can be reduced to itself by a Turing machine that does not ask its own input to the oracle. We use autoreducibility to separate the polynomial-time hierarchy from exponential space by showing that all Turing complete sets for certain levels of the exponential-time hierarchy are autoreducible but there exists some Turing complete set for doubly exponential space that is not.Although we already knew how to separate these classes using diagonalization, our proofs separate classes solely by showing they have different structural properties, thus applying Post's program to complexity theory. We feel such techniques may prove unknown separations in the future. In particular, if we could settle the question as to whether all Turing complete sets for doubly exponential time are autoreducible, we would separate either polynomial time from polynomial space, and nondeterministic logarithmic space from nondeterministic polynomial time, or else the polynomial-time hierarchy from exponential time.We also look at the autoreducibility of complete sets under nonadaptive, bounded query, probabilistic, and nonuniform reductions. We show how settling some of these autoreducibility questions will also lead to new complexity class separations.