Phase Transition between Unidirectionality and Bidirectionality

  • Kohtaro Tadaki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7160)


The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration enables us to deal with the notion of asymptotic behavior in a manner like in computational complexity theory, while staying in computability theory. We apply the elaboration to sets which appear in the statistical mechanical interpretation of algorithmic information theory. We demonstrate the power of the elaboration by revealing a critical phenomenon, i.e., a phase transition, in the statistical mechanical interpretation, which cannot be captured by the original notion of weak truth-table reducibility.


Binary String Recursive Function Order Function Recursion Theory Consecutive Zero 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kohtaro Tadaki
    • 1
  1. 1.Research and Development InitiativeChuo University, JST CRESTBunkyo-kuJapan

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