Computations with Uncertain Time Constraints: Effects on Parallelism and Universality

  • Naya Nagy
  • Selim G. Akl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6714)


We introduce the class of problems with uncertain time constraints. The first type of time constraints refers to uncertain time requirements on the input, that is, when and for how long are the input data available. A second type of time constraints refers to uncertain deadlines for tasks. Our main objective is to exhibit computational problems in which it is very difficult to find out (read ‘compute’) what to do and when to do it. Furthermore, problems with uncertain time constraints, as described here, prove once more that it is impossible to define a ‘universal computer’, that is, a computer able to compute all computable functions. Finally, one of the contributions of this paper is to promote the study of a topic, conspicuously absent to date from theoretical computer science, namely, the role of physical time and physical space in computation. The focus of our work is to analyze the effect of external natural phenomena on the various components of a computational process, namely, the input phase, the calculation phase (including the algorithm and the computing agents themselves), and the output phase.


real-time computation unconventional computation Turing Machine universal computer parallel computing physical time physical space external phenomena 


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  1. 1.
    Akl, S.G.: Universality in computation: Some quotes of interest. Technical Report No. 2006-511, School of Computing, Queen’s University, Kingston, Ontario (2006)Google Scholar
  2. 2.
    Akl, S.G.: Three counterexamples to dispel the myth of the universal computer. Parallel Processing Letters 16, 381–403 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Akl, S.G.: Even accelerating machines are not universal. International Journal of Unconventional Computing 3, 105–121 (2007)Google Scholar
  4. 4.
    Akl, S.G.: Evolving Computational Systems. In: Rajasekaran, S., Reif, J.H. (eds.) Handbook of Parallel Computing: Models, Algorithms, and Applications, pp. 1–22. Taylor and Francis, CRC Press, Boca Raton (2008)Google Scholar
  5. 5.
    Akl, S.G.: Unconventional Computational Problems with Consequences to Universality. International Journal of Unconventional Computing 4, 89–98 (2008)Google Scholar
  6. 6.
    Akl, S.G.: Ubiquity and Simultaneity: The Science and Philosophy of Space and Time in Unconventional Computation. Invited talk, Conference on the Science and Philosophy of Unconventional Computing. The University of Cambridge, Cambridge (2009)Google Scholar
  7. 7.
    Akl, S.G.: Time travel: A New Hypercomputational Paradigm. International Journal of Unconventional Computing 6, 329–351 (2011)Google Scholar
  8. 8.
    Bruda, S.D., Akl, S.G.: The Characterization of Data-Accumulating Algorithms. Theory of Computing Systems 33, 85–96 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Buttazzo, G.C.: Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications. Kluwer Academic Publishers, Boston (1997)zbMATHGoogle Scholar
  10. 10.
    Buttazzo, G.C.: Soft Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications. Springer, New York (2005)CrossRefzbMATHGoogle Scholar
  11. 11.
    Calude, C.S., Păun, G.: Bio-Steps Beyond Turing. BioSystems 77, 175–194 (2004)CrossRefGoogle Scholar
  12. 12.
    Deutsch, D.: The Fabric of Reality. Penguin Books, London (1997)Google Scholar
  13. 13.
    Etesi, G., Németi, I.: Non-Turing Computations via Malament-Hogarth Space-Times. International Journal of Theoretical Physics 41, 341–370 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Nagy, M., Akl, S.G.: Quantum Measurements and Universal Computation. International Journal of Unconventional Computing 2, 73–88 (2006)Google Scholar
  15. 15.
    Siegelmann, H.T.: Neural Networks and Analog Computation: Beyond the Turing limit. Birkhäuser, Boston (1999)CrossRefzbMATHGoogle Scholar
  16. 16.
    Stannet, M.: X-machines and the Halting Problem: Building a Super-Turing Machine. Formal Aspects of Computing 2, 331–341 (1990)CrossRefGoogle Scholar
  17. 17.
    Wegner, P., Goldin, D.: Computation Beyond Turing Machines. Communications of the ACM 46, 100–102 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Naya Nagy
    • 1
  • Selim G. Akl
    • 1
  1. 1.School of ComputingQueen’s UniversityKingstonCanada

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