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The Complexity of Satisfiability of Small Depth Circuits

  • Chris Calabro
  • Russell Impagliazzo
  • Ramamohan Paturi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5917)

Abstract

Say that an algorithm solving a Boolean satisfiability problem x on n variables is improved if it takes time poly(|x|)2 cn for some constant c < 1, i.e., if it is exponentially better than a brute force search. We show an improved randomized algorithm for the satisfiability problem for circuits of constant depth d and a linear number of gates cn: for each d and c, the running time is 2(1 − δ)n where the improvement \(\delta\geq 1/O(c^{2^{d-2}-1}\lg^{3\cdot 2^{d-2}-2}c)\), and the constant in the big-Oh depends only on d. The algorithm can be adjusted for use with Grover’s algorithm to achieve a run time of \(2^{\frac{1-\delta}{2}n}\) on a quantum computer.

Keywords

Success Probability Block Cipher Satisfying Assignment Depth Circuit Exact Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Chris Calabro
    • 1
  • Russell Impagliazzo
    • 1
  • Ramamohan Paturi
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of CaliforniaSan Diego, La JollaUSA

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