The Minimum Oracle Circuit Size Problem

Eric Allender, Dhiraj Holden, Valentine Kabanets

Research output: Contribution to journalArticle

13 Scopus citations


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 MSCPQBF 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 TC0 under uniform AC0 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.

Original languageEnglish (US)
Pages (from-to)469-496
Number of pages28
JournalComputational Complexity
Issue number2
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics(all)
  • Computational Theory and Mathematics
  • Computational Mathematics


  • F.1.3 Complexity Measures and Classes
  • Kolmogorov complexity
  • Minimum circuit size problem
  • NP-intermediate sets

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