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On the Autoreducibility of Random Sequences

  • Todd Ebert
  • Heribert Vollmer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)

Abstract

A language A⊂- {0, 1}* is called i.o. autoreducible if A is Turing-reducible to itself via a machine M such that, for infinitely many input words w, M does not query its oracle A about w. We examine the question if algorithmically random languages in the sense of Martin-Löf are i.o. autoreducible. We obtain the somewhat counterintuitive result that every algorithmically random language is polynomial-time i.o. auto-reducible where the autoreducing machine poses its queries in a “quasi-nonadaptive” way; however, if in the above definition the “infinitely many” is replaced by “almost all,” then every algorithmically random language is not autoreducible in this stronger sense. Further results obtained give upper and lower bounds on the number of queries of the autoreducing machine M and the number of inputs w for which M does not query the oracle about w.

Keywords

Random Sequence Turing Machine Binary Sequence Recursive Function Code Word 
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 2000

Authors and Affiliations

  • Todd Ebert
    • 1
  • Heribert Vollmer
    • 2
  1. 1.DoCoMo Communications Laboratories, USAPalo Alto
  2. 2.Theoretische InformatikUniversität WürzburgWürzburgGermany

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