Abstract
We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts.
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References
Amoroso, S., Patt, Y.N.: Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures. J. Comput. System Sci. 6, 448–464 (1972)
Aubrun, N.: Dynamique symbolique des systèmes 2D et des arbres infinis. Ph.D. thesis, Universitè Paris-Est (2011)
Aubrun, N., Béal, M.-P.: Sofic and Almost of Finite Type Tree-Shifts. In: Ablayev, F., Mayr, E.W. (eds.) CSR 2010. LNCS, vol. 6072, pp. 12–24. Springer, Heidelberg (2010)
Aubrun, N., Béal, M.P.: Sofic tree-shifts (to appear, 2012)
Ceccherini-Silberstein, T., Coornaert, M.: Cellular Automata and Groups. Springer Monographs in Mathematics, Berlin (2010)
Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007), http://www.grappa.univ-lille3.fr/tata
Fiorenzi, F.: Cellular automata and strongly irreducible shifts of finite type. Theoret. Comput. Sci. 299(1-3), 477–493 (2003)
Kari, J.: Reversibility and surjectivity problems of cellular automata. J. Comput. System Sci. 48(1), 149–182 (1994)
Lind, D.A., Marcus, B.H.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995)
Muller, D.E., Schupp, P.E.: The theory of ends, pushdown automata, and second-order logic. Theoret. Comput. Sci. 37(1), 51–75 (1985)
Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Trans. Am. Math. Soc. 141, 1–35 (1969)
Thatcher, J.W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Syst. Theory
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Ceccherini-Silberstein, T., Coornaert, M., Fiorenzi, F., Šunić, Z. (2012). Cellular Automata on Regular Rooted Trees. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_9
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DOI: https://doi.org/10.1007/978-3-642-31606-7_9
Publisher Name: Springer, Berlin, Heidelberg
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