Randomized Gandy-Păun-Rozenberg Machines

  • Adam Obtułowicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6501)


An idea of a randomized Gandy–Păun–Rozenberg machine providing a certain abstract implementation of concurrent (parallel) randomized algorithms is introduced. A randomized Gandy–Păun–Rozenberg machine for solving 3-SAT problem in a polynomial time with the low error probability and with subexponential number of indecomposable processors is shown. This machine assembles a distributed system which then realizes a massively parallel computation.


Polynomial Time Turing Machine Binary String Conjunctive Normal Form Truth Assignment 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chi, H., Jones, E.L.: Generating parallel quasirandom sequences via randomization. J. Parallel Distrib. Comput. 67, 876–881 (2007)CrossRefzbMATHGoogle Scholar
  2. 2.
    Gandy, R.: Church’s thesis and principles for mechanisms. In: Barwise, J., et al. (eds.) The Kleene Symposium, pp. 123–148. North-Holland, Amsterdam (1980)CrossRefGoogle Scholar
  3. 3.
    Rozenberg, G.: Handbook of graph grammars and computing by graph transformation, vol. 1. World Scientific, River Edge (1997); Ehrig, H. et al., Applications, languages and tools, vol. 2. World Scientific, River Edge (1999); Ehrig, H., et al., Concurrency, parallelism, and distribution, vol. 3. World Scientific, River Edge (1999)CrossRefzbMATHGoogle Scholar
  4. 4.
    Koblitz, N.: Algebraic Aspects of Cryptography, Berlin (1998)Google Scholar
  5. 5.
    Obtułowicz, A.: Gandy–Păun–Rozenberg machines. Romanian J. of Information Science and Technology 13, 181–196 (2010)zbMATHGoogle Scholar
  6. 6.
    Papadimitriou, G.: Computational Complexity. Addison–Wesley, Reading (1994)zbMATHGoogle Scholar
  7. 7.
    Păun, G.: P systems with active membranes: Attacking NP complete problems. Journal of Automata, Languages and Combinatorics 6, 75–90 (2000)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Păun, G.: Membrane Computing. An Introduction, Berlin (2002)Google Scholar
  9. 9.
    Sieg, W., Byrnes, J.: An abstract model for parallel computations: Gandy’s Thesis. The Monist 82(1), 150–164 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Adam Obtułowicz
    • 1
  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland

Personalised recommendations