Abstract
We study iterated transductions defined by a class of invertible transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.
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References
Bartholdi, L., Silva, P.V.: Groups defined by automata. CoRR, abs/1012.1531 (2010)
Berstel, J.: Transductions and context-free languages (2009), http://www-igm.univ-mlv.fr/~berstel/LivreTransductions/LivreTransductions.html
Brzozowski, J.A.: Derivatives of regular expressions. Journal Assoc. for Comp. Machinery 11 (1964)
Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press (1974)
Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM J. Res. Dev. 9, 47–68 (1965)
Epstein, D.B.A., Cannon, J.W., Holt, D.F., Levy, S.V.F., Patterson, M.S., Thurston, W.P.: Word Processing in Groups. Jones and Bartlett (1992)
Gluškov, V.M.: Abstract theory of automata. Uspehi Mat. Nauk 16(5(101)), 3–62 (1961)
Gouvêa, F.Q.: p-Adic Numbers: An Introduction, 2nd edn. Springer (1997)
Grigorchuk, R.R., Nekrashevich, V.V., Sushchanski, V.I.: Automata, dynamical systems and groups. Proc. Steklov Institute of Math. 231, 128–203 (2000)
Kharlampovich, O., Khoussainov, B.: A Miasnikov. From automatic structures to automatic groups. ArXiv e-prints (July 2011)
Khoussainov, B., Nerode, A.: Automatic Presentations of Structures. In: Leivant, D. (ed.) LCC 1994. LNCS, vol. 960, pp. 367–392. Springer, Heidelberg (1995)
Khoussainov, B., Nerode, A.: Automata Theory and its Applications. Birkhäuser (2001)
Khoussainov, B., Rubin, S.: Automatic structures: overview and future directions. J. Autom. Lang. Comb. 8(2), 287–301 (2003)
Knuth, D.: Private communication (2010)
Nekrashevych, V.: Self-Similar Groups. Math. Surveys and Monographs, vol. 117. AMS (2005)
Nekrashevych, V., Sidki, S.: Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms. Cambridge University Press (2004)
Raney, G.N.: Sequential functions. J. Assoc. Comp. Mach. 5(2), 177–180 (1958)
Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press (2009)
Serre, J.-P.: Arbres, Amalgames, SL 2. Number 46 in Astérisque. Société Mathématique de France, Paris (1977)
Sidki, S.: Automorphisms of one-rooted trees: Growth, circuit structure, and acyclicity. J. Math. Sciences 100(1), 1925–1943 (2000)
Sutner, K., Devanny, W.: Timestamps in iterated invertible transducers (in preparation, 2012)
Vuillemin, J.: On circuits and numbers. IEEE Transactions on Computers 43, 868–879 (1994)
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Sutner, K., Lewi, K. (2012). Iterating Invertible Binary Transducers. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_23
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DOI: https://doi.org/10.1007/978-3-642-31623-4_23
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