Separating complexity classes using autoreducibility
Abstract
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 polynomialtime hierarchy from polynomial space by showing that all Turingcomplete sets for certain levels of the exponentialtime hierarchy are autoreducible but there exists some Turingcomplete 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 Turingcomplete 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 polynomialtime 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 read to new complexity class separations.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1998
 DOI:
 10.48550/arXiv.math/9807185
 arXiv:
 arXiv:math/9807185
 Bibcode:
 1998math......7185B
 Keywords:

 Mathematics  Logic