A Simple and Efficient Universal Reversible Turing Machine

  • Holger Bock Axelsen
  • Robert Glück
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6638)


We construct a universal reversible Turing machine (URTM) from first principles. We take a strict approach to the semantics of reversible Turing machines (RTMs), under which they can compute exactly all injective, computable functions, but not non-injective ones. The natural notion of universality for RTMs is RTM-universality, where programs are considered part of both input and output of a URTM.

The machine described here is the first URTM which does not depend on reversibilizing any existing universal machine. The interpretive overhead of the URTM is limited to a (program dependent) constant factor slowdown, with no other complexity-wise cost wrt time and space. The URTM is also able to function as an inverse interpreter for RTMs at no asymptotic cost, simply by reversing the string representing the interpreted machine.


Turing Machine Program Text Asymptotic Complexity Universal Machine Move Rule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Holger Bock Axelsen
    • 1
  • Robert Glück
    • 1
  1. 1.DIKU, Department of Computer ScienceUniversity of CopenhagenDenmark

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