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Theory of Computing Systems

, Volume 46, Issue 3, pp 479–498 | Cite as

A Search Algorithm for Subshift Attractors of Cellular Automata

  • Enrico Formenti
  • Petr Kůrka
  • Ondřej Zahradník
Article

Abstract

We describe a heuristic algorithm which searches for spreading clopen sets of a cellular automaton. Then the algorithms searches for the corresponding subshift attractors (which are omega-limits of spreading sets found) as forward images of joins of signal subshifts.

Keywords

Sofic subshifts Subshift attractors Spreading sets Signal subshifts 

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References

  1. 1.
    Kůrka, P.: On the measure attractor of a cellular automaton. Discrete Continuous Dyn. Syst. 2005, 524–535 (2005) Supplement volume zbMATHGoogle Scholar
  2. 2.
    Formenti, E., Kůrka, P.: Subshift attractors of cellular automata. Nonlinearity 20, 105–117 (2007) zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Culik, K., Pachl, J., Yu, S.: On the limit set of cellular automata. SIAM J. Comput. 18(4), 831–842 (1989) zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Maass, A.: On the sofic limit set of cellular automata. Ergod. Theory Dyn. Syst. 15, 663–684 (1995) zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kari, J.: The nilpotency problem of one-dimensional cellular automata. SIAM J. Comput. 21(3), 571–586 (1992) zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Formenti, E., Kůrka, P.: A search algorithm for the maximal attractor of a cellular automaton. In: Thomas, W., Weil, P. (eds.) STACS 2007, vol. 4393, pp. 356–366. Springer, Berlin (2007) CrossRefGoogle Scholar
  7. 7.
    Boyle, M., Kitchens, B.: Periodic points for onto cellular automata. Indag. Math. 10(4), 483–493 (1999) zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Hopcroft, J.E., Ullmann, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979) zbMATHGoogle Scholar
  9. 9.
    Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995) zbMATHCrossRefGoogle Scholar
  10. 10.
    Kitchens, B.P.: Symbolic Dynamics. Springer, Berlin (1998) zbMATHGoogle Scholar
  11. 11.
    Kari, J.: The Rice’s theorem for the limit sets of cellular automata. Theor. Comput. Sci. 127, 229–254 (1994) zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Tarjan, R.: Depth-first search and linear search algorithms. SIAM J. Comput. 1, 146–160 (1972) zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Knuutila, T.: Re-describing an algorithm by Hopcroft. Theor. Comput. Sci. 250, 333–363 (2001) zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Comput. 22(6), 1117–1141 (1993) zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Ilie, L., Yu, S.: Reducing NFAs by invariant equivalences. Theor. Comput. Sci. 306, 373–390 (2003) zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Ilie, L., Solis-Oba, R., Yu, S.: Reducing NFAs by equivalences and preorders. In: Apostolico, A., Crochemore, M., Park, K. (eds.) Proceedings of the 16th CPM, Jeju Island, Korea, 2005. Lecture Notes in Computer Science, vol. 3537, pp. 310–321. Springer, Berlin (2005) Google Scholar
  17. 17.
    Ilie, L., Navarro, G., Yu, S.: On NFA reductions. In: Karhumaki, J. (ed.) Theory Is Forever (Salomaa Festschrift). Lecture Notes in Computer Science, vol. 3113, pp. 112–124. Springer, Berlin (2004) Google Scholar
  18. 18.
    Champarnaud, J.M., Coulon, F.: NFA reduction algorithms by means of regular inequalities. Theor. Comput. Sci. 327(3), 241–253 (2004) CrossRefMathSciNetGoogle Scholar
  19. 19.
    Champarnaud, J.M., Coulon, F.: NFA reduction algorithms by means of regular inequalities—correction. Erratum in Theor. Comput. Sci. (2005) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Enrico Formenti
    • 1
  • Petr Kůrka
    • 1
    • 2
  • Ondřej Zahradník
    • 3
  1. 1.Laboratoire I3SUniversité de Nice-Sophia AntipolisSophia Antipolis CedexFrance
  2. 2.Center for Theoretical StudyAcademy of Sciences and Charles University in PraguePraha 1Czech Republic
  3. 3.Faculty of Mathematics and PhysicsCharles University in PraguePraha 1Czech Republic

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