The Minimum Oracle Circuit Size Problem

Author(s)
Allender, Eric; Holden, Dhiraj; Kabanets, Valentine
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Abstract
We consider variants of the minimum circuit size problem MCSP, where the goal is to minimize the size of oracle circuits computing a given function. When the oracle is QBF, the resulting problem MSCP[superscript QBF] is known to be complete for PSPACE under ZPP reductions. We show that it is not complete under logspace reductions, and indeed it is not even hard for TC[superscript 0] under uniform AC[superscript 0] reductions. We obtain a variety of consequences that follow if oracle versions of MCSP are hard for various complexity classes under different types of reductions. We also prove analogous results for the problem of determining the resource-bounded Kolmogorov complexity of strings, for certain types of Kolmogorov complexity measures.
Date issued
2016-02
URI
http://hdl.handle.net/1721.1/106913
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
computational complexity
Publisher
Springer International Publishing
Citation
Allender, Eric, Dhiraj Holden, and Valentine Kabanets. “The Minimum Oracle Circuit Size Problem.” Comput. Complex. (February 17, 2016).
Version: Author's final manuscript
ISSN
1016-3328
1420-8954
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