The Minimum Oracle Circuit Size Problem
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37_2016_Article_124.pdf
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Author(s)
Allender, Eric
Holden, Dhiraj
Kabanets, Valentine
Date Issued
February 2016
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
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00037-016-0124-0
