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A Counting Equivalence Classes Method to Prove Negative Results

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Cellular Automata

Part of the book series: Mathematics and Its Applications ((MAIA,volume 460))

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Abstract

In this paper we review the techniques developed to prove limitation on the real time recognition ability of Iterative Array and One-way Cellular Automata. The different proofs are based on the same principle which uses equivalence relations and counting arguments.

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References

  • Choffrut C. and Culik K. On real time cellular automata and trellis automata. Acta Informatica Vol. no. 21: 393–407, 1984.

    Google Scholar 

  • Cole S. Real-time computation by n-dimensional iterative arrays of finite-state machine. IEEE Trans. Comput.Vol. no. C-18: 349–365, 1969.

    Google Scholar 

  • Culik K., Gruska J. and Salomaa A. Systolic trellis automata (for VLSI). Res. Rep. CS-81–34 Dept. of Comput. Sci., University of Waterloo, Vol. no. 34, 1981.

    Google Scholar 

  • Hartmanis J. and Stearns R. On the computational complexity of algorithms. Trans.Amer. Math. Soc. Vol. 117 no. 5: 285–306, 1965.

    Google Scholar 

  • Ibarra O. and Jiang T. On the computational complexity of algorithms. Theoretical Computer Science Vol. no. 57: 225–238, 1988.

    Google Scholar 

  • Rosenberg A. Real-time definable languages. J. ACM Vo1.14 no. 4: 645–662, 1967.

    Google Scholar 

  • Smith A. Cellular Automata and formal languages. Proc. 11th IEEE Ann. Symp. Switching Automata Theory vol. 14 no. 4: 216–224, 1970.

    Google Scholar 

  • Smith A. Real-time language recognition by one-dimensional cellular automata. J. Comput. System Sci Vol. no. 6: 233–253, 1972.

    Google Scholar 

  • Terrier V. On real time one-way cellular automata. Theoretical Computer Science Vol. no. 141: 331–335, 1995.

    Google Scholar 

  • Terrier V. Language not recognizable in real time by one-way cellular automata. Theoretical Computer Science Vol. no. 156: 281–287, 1996.

    Google Scholar 

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© 1999 Springer Science+Business Media Dordrecht

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Terrier, V. (1999). A Counting Equivalence Classes Method to Prove Negative Results. In: Delorme, M., Mazoyer, J. (eds) Cellular Automata. Mathematics and Its Applications, vol 460. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9153-9_7

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  • DOI: https://doi.org/10.1007/978-94-015-9153-9_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5143-1

  • Online ISBN: 978-94-015-9153-9

  • eBook Packages: Springer Book Archive

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