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A Note on polynomial-size circuits with low resource-bounded Kolmogorov complexity

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Abstract

It is well known that the class P/poly can be characterized in terms of polynomial-size circuits. We obtain a characterization of the class P/log using polynomial-size circuits with low resource-bounded Kolmogorov complexity.

The concept of “small circuits with easy descriptions” has been introduced in the literature as a candidate for characterizing P/log. We prove that this concept corresponds exactly to the class P/O(log n * log(log n)), and that this is different from P/log.

Generalizations of this result are also obtained.

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Authors and Affiliations

  1. Departamento de Lenguajes y Sistemas Informáticos, Universidad del Pais Vasco, E-20080, San Sebastian, Spain

    Montserrat Hermo

  2. Departament de Llenguatges i Sistemes Informatics, Universitat Politècnica de Catalunya, Pau Gargallo 5, E-08028, Barcelona, Spain

    Elvira Mayordomo

Authors
  1. Montserrat Hermo
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  2. Elvira Mayordomo
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Hermo, M., Mayordomo, E. A Note on polynomial-size circuits with low resource-bounded Kolmogorov complexity. Math. Systems Theory 27, 347–356 (1994). https://doi.org/10.1007/BF01192144

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  • DOI: https://doi.org/10.1007/BF01192144

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