Abstract
We define the class of sofic-Dyck shifts which extends the class of Markov-Dyck shifts introduced by Krieger and Matsumoto. The class of sofic-Dyck shifts is a particular class of shifts of sequences whose finite factors are unambiguous context-free languages. We show that it corresponds exactly to shifts of sequences whose set of factors is a visibly pushdown language. We give an expression of the zeta function of a sofic-Dyck shift which has a deterministic presentation.
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References
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 202–211. ACM, New York (2004) (electronic)
Alur, R., Madhusudan, P.: Adding nesting structure to words. J. ACM 56(3) (2009)
Béal, M.-P., Blockelet, M., Dima, C.: Zeta function of finite-type Dyck shifts are ℕ-algebraic. In: Information Theory and Applications Workshop (2014)
Berstel, J., Boasson, L.: Balanced grammars and their languages. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 3–25. Springer, Heidelberg (2002)
Berstel, J., Perrin, D., Reutenauer, C.: Codes and automata. Encyclopedia of Mathematics and its Applications, vol. 129. Cambridge University Press, Cambridge (2010)
Bowen, R.: Symbolic dynamics. In: On axiom A Diffeomorphism. CBMS Reg. Conf. American Mathematical Society, vol. (35) (1978)
Bowen, R., Lanford, O.: Zeta functions of restrictions of the shift transformation. In: Proc. Sympos. Pure Math., vol. 14, pp. 43–50. American Mathematical Society (1970)
Culik II, K., Yu, S.: Cellular automata, ωω-regular sets, and sofic systems. Discrete Appl. Math. 32(2), 85–101 (1991)
Ginsburg, S., Harrison, M.A.: Bracketed context-free languages. J. Comput. Syst. Sci. 1(1), 1–23 (1967)
Hamachi, T., Krieger, W.: On certain subshifts and their associated monoids. CoRR, abs/1202.5207 (2013)
Inoue, K.: The zeta function, periodic points and entropies of the Motzkin shift. CoRR, math/0602100 (2006)
Inoue, K., Krieger, W.: Subshifts from sofic shifts and Dyck shifts, zeta functions and topological entropy. CoRR, abs/1001 (2010)
Keller, G.: Circular codes, loop counting, and zeta-functions. J. Combin. Theory Ser. A 56(1), 75–83 (1991)
Krieger, W.: On subshift presentations. CoRR, abs/1209.2578 (2012)
Krieger, W., Matsumoto, K.: Zeta functions and topological entropy of the Markov-Dyck shifts. Münster J. Math. 4, 171–183 (2011)
Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995)
Manning, A.: Axiom A diffeomorphisms have rationnal zeta fonctions. Bull. London Math. Soc. 3, 215–220 (1971)
McNaughton, R.: Parenthesis grammars. J. ACM 14(3), 490–500 (1967)
Reutenauer, C.: ℕ-rationality of zeta functions. Adv. in Appl. Math. 18(1), 1–17 (1997)
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Béal, MP., Blockelet, M., Dima, C. (2014). Sofic-Dyck Shifts. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_6
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DOI: https://doi.org/10.1007/978-3-662-44522-8_6
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