Lower Bounds Using Kolmogorov Complexity

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Lower Bounds Using Kolmogorov Complexity
Abstract. In this paper, we survey a few recent applications of Kolmogorov complexity to lower bounds in several models of computation. We consider KI complexity of Boolean functions, which gives the complexity of finding a bit where inputs differ, for pairs of inputs that map to different function values. This measure and variants thereof were shown to imply lower bounds for quantum and randomized decision tree complexity (or query complexity) [LM04]. We give a similar result for deterministic decision trees as well. It was later shown in [LLS05] that KI complexity gives lower bounds for circuit depth. We review those results here, emphasizing simple proofs using Kolmogorov complexity, instead of strongest possible lower bounds. We also present a Kolmogorov complexity alternative to Yao's min-max principle [LL04]. As an example, this is applied to randomized one-way communication complexity.
Sophie Laplante
Added 20 Aug 2010
Updated 20 Aug 2010
Type Conference
Year 2006
Where CIE
Authors Sophie Laplante
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