Abstract
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.
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© 1996 Springer-Verlag Berlin Heidelberg
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Kummer, M. (1996). On the complexity of random strings. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_3
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DOI: https://doi.org/10.1007/3-540-60922-9_3
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