The Minimum Oracle Circuit Size Problem

Authors Eric Allender, Dhiraj Holden, Valentine Kabanets

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Eric Allender
Dhiraj Holden
Valentine Kabanets

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Eric Allender, Dhiraj Holden, and Valentine Kabanets. The Minimum Oracle Circuit Size Problem. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 21-33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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 MCSP^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 under uniform AC^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.
  • Kolmogorov complexity
  • minimum circuit size problem
  • NP-intermediate sets


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