On the complexity of random strings

Extended abstract
  • Martin Kummer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


We show that the set R of Kolmogorov random strings is truth-table complete. This improves the previously known Turing completeness of R and shows how the halting problem can be encoded into the distribution of random strings rather than using the time complexity of non-random strings. As an application we obtain that Post's simple set is truth-table complete in every Kolmogorov numbering. We also show that the truth-table completeness of R cannot be generalized to size-complexity with respect to arbitrary acceptable numberings. In addition we note that R is not frequency computable.


Boolean Function Recursive Function Winning Strategy Kolmogorov Complexity Random String 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Martin Kummer
    • 1
  1. 1.Institut für Logik, Komplexität und DeduktionssystemeUniversität KarlsruheKarlsruheGermany

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