Turing machines on cayley graphs

  • Authors:

  • Aubrey da Cunha

  • Affiliations:

  • University of Michigan, Ann Arbor, MI

  • Venue:
  • WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
  • Year:
  • 2011

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Abstract

We present a generalization of standard Turing machines based on allowing unusual tapes. We present a set of reasonable constraints on tape geometry and conclude that the proper degree of generality is Cayley graphs. Surprisingly, this generalization does not lead to yet another equivalent formulation of the notion of computable function. Rather, it gives an alternative definition of the recursively enumerable Turing degrees that does not rely on oracles