Using Depth to Capture Average-Case Complexity

Luis Antunes, Lance Fortnow, N. V. Vinodchandran

Abstract: We give the first characterization of Turing machines that run in polynomial-time on average. We show that a Turing machine M runs in average polynomial-time if for all inputs x the Turing machine uses time exponential in the computational depth of x, where the computational depth is a measure of the amount of “useful” information in x.