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Resource-bounded Kolmogorov complexity of hard languages

Extended abstract
  • Dung T. Huynh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 223)

Abstract

This paper explores further the relationship between randomness and complexity. The concept of time-/space-bounded Kolmogorov complexity of languages is introduced. Among others we show that there exists a language L in DTIME(22lin) such that the 2poly-time-bounded Kolmogorov complexity of L is exponential almost everywhere. We study time-/space- bounded Kolmogorov complexity of languages that are DTIME(22lin)-(SPACE (2lin)-) hard under polynomial-time Turing reductions. The connection between Kolmogorov-random languages and almost everywhere hard languages is investigated. We also show that Kolmogorov randomness implies Church randomness. Finally, we work out the relationship between time-/space- bounded Kolmogorov complexity and time-/space- bounded descriptional complexity of Boolean circuits and formulas for hard languages. This result provides a classification of exponential-size circuits and formulas in terms of the amount of information contained in them.

Keywords

Binary String Boolean Formula Kolmogorov Complexity Input Instance Boolean Circuit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Dung T. Huynh
    • 1
  1. 1.Computer Science DepartmentIowa State UniversityAmes

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