computational complexity

, Volume 26, Issue 2, pp 469–496 | Cite as

The Minimum Oracle Circuit Size Problem

  • Eric Allender
  • Dhiraj Holden
  • Valentine KabanetsEmail author


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 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 0 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.

Subject classification

F.1.3 Complexity Measures and Classes 


Kolmogorov complexity Minimum circuit size problem PSPACE NP-intermediate sets 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Eric Allender
    • 1
  • Dhiraj Holden
    • 2
  • Valentine Kabanets
    • 3
    Email author
  1. 1.Department of Computer ScienceRutgers UniversityPiscatawayUSA
  2. 2.CSAILMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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