An Analogue-Digital Model of Computation: Turing Machines with Physical Oracles

  • Tânia AmbaramEmail author
  • Edwin Beggs
  • José Félix Costa
  • Diogo Poças
  • John V. Tucker
Part of the Emergence, Complexity and Computation book series (ECC, volume 22)


We introduce an abstract analogue-digital model of computation that couples Turing machines to oracles that are physical processes. Since any oracle has the potential to boost the computational power of a Turing machine, the effect on the power of the Turing machine of adding a physical process raises interesting questions. Do physical processes add significantly to the power of Turing machines; can they break the Turing Barrier? Does the power of the Turing machine vary with different physical processes? Specifically, here, we take a physical oracle to be a physical experiment, controlled by the Turing machine, that measures some physical quantity. There are three protocols of communication between the Turing machine and the oracle that simulate the types of error propagation common to analogue-digital devices, namely: infinite precision, unbounded precision, and fixed precision. These three types of precision introduce three variants of the physical oracle model. On fixing one archetypal experiment, we show how to classify the computational power of the three models by establishing the lower and upper bounds. Using new techniques and ideas about timing, we give a complete classification.


Turing Machine Physical Time Explicit Time Boundary Number Vertex Position 
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.



To Bill Tantau for the use of pgf/TikZ applications.


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Tânia Ambaram
    • 1
    Email author
  • Edwin Beggs
    • 2
  • José Félix Costa
    • 1
  • Diogo Poças
    • 3
  • John V. Tucker
    • 2
  1. 1.Department of MathematicsInstituto Superior Técnico, Universidade de LisboaLisboaPortugal
  2. 2.College of ScienceSwansea UniversityWalesUK
  3. 3.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

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