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Symmetry of information and nonuniform lower bounds

Abstract

In the first part we provide another proof of the result of [Homer, Mocas 1995] that for all constant c, the class EXP is not included in P/(n^c) . The proof is based on a simple diagonalization, whereas it uses resource-bounded Kolmogorov complexity in [Homer, Mocas 1995]. In the second part, we investigate links between resource-bounded Kolmogorov complexity and nonuniform classes in computational complexity. Assuming a version of polynomial-time symmetry of information, we show that exponential-time problems do not have polynomial-size circuits (in symbols, EXP is not included in P/poly).
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Dates and versions

ensl-00119823 , version 1 (12-12-2006)
ensl-00119823 , version 2 (04-06-2007)

Identifiers

  • HAL Id : ensl-00119823 , version 2

Cite

Sylvain Perifel. Symmetry of information and nonuniform lower bounds. 2007. ⟨ensl-00119823v2⟩
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