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  1. Polynomial local search in the polynomial hierarchy and witnessing in fragments of bounded arithmetic.Arnold Beckmann & Samuel R. Buss - 2009 - Journal of Mathematical Logic 9 (1):103-138.
    The complexity class of [Formula: see text]-polynomial local search problems is introduced and is used to give new witnessing theorems for fragments of bounded arithmetic. For 1 ≤ i ≤ k + 1, the [Formula: see text]-definable functions of [Formula: see text] are characterized in terms of [Formula: see text]-PLS problems. These [Formula: see text]-PLS problems can be defined in a weak base theory such as [Formula: see text], and proved to be total in [Formula: see text]. Furthermore, the [Formula: (...)
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