Dimension Characterizations of Complexity Classes

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Xiaoyang Gu, Jack H. Lutz

Published: 2006, Last Modified: 27 Jan 2026MFCS 2006EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We use derandomization to show that sequences of positive pspace-dimension – in fact, even positive Δ\(^{\rm p}_{\rm k}\)-dimension for suitable k – have, for many purposes, the full power of random oracles. For example, we show that, if S is any binary sequence whose Δ\(^{\rm p}_{\rm 3}\)-dimension is positive, then BPP ⊆ PS and, moreover, every BPP promise problem is PS-separable. We prove analogous results at higher levels of the polynomial-time hierarchy.