Abstract
It has been shown that every tree automatic structure admits an injective tree automatic presentation, but no good size or time bounds are known. From an arbitrary tree automatic presentation, we construct an equivalent injective one in polynomial space that consequently has exponential size. Furthermore we also prove an exponential lower bound for the size of injective tree automatic presentations.
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References
Blumensath, A.: Automatic structures. Diplomarbeit, RWTH Aachen (1999)
Blumensath, A., Grädel, E.: Automatic Structures. In: LICS 2000, pp. 51–62. IEEE Computer Society Press, Los Alamitos (2000)
Colcombet, T., Löding, C.: Transforming structures by set interpretations. Logical Methods in Computer Science 3(2) (2007)
Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications, http://www.grappa.univ-lille3.fr/tata (release October 12, 2007),
Hodgson, B.R.: On direct products of automaton decidable theories. Theor. Comput. Sci. 19, 331–335 (1982)
Kartzow, A.: Collapsible pushdown graphs of level 2 are tree-automatic. In: STACS 2010, Leibniz International Proceedings in Informatics (LIPIcs), vol. 5, pp. 501–512. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2010)
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., Nies, A., Rubin, S., Stephan, F.: Automatic structures: Richness and limitations. Logical Methods in Computer Science 3(2) (2007)
Khoussainov, B., Rubin, S., Stephan, F.: Definability and Regularity in Automatic Structures. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 440–451. Springer, Heidelberg (2004)
Khoussainov, B., Rubin, S., Stephan, F.: Automatic linear orders and trees. ACM Trans. Comput. Log. 6(4), 675–700 (2005)
Kuske, D., Lohrey, M.: Automatic structures of bounded degree revisited. To appear in Journal of Symbolic Logic in slightly extended form (2008), http://arxiv.org/abs/0810.4998
Kuske, D., Lohrey, M.: Some natural problems in automatic graphs. J. Symbolic Logic 75(2), 678–710 (2010)
Kuske, D., Liu, J., Lohrey, M.: The isomorphism problem on classes of automatic structures. In: LICS 2010, pp. 160–169. IEEE Computer Society, Los Alamitos (2010)
To, A.W., Libkin, L.: Recurrent Reachability Analysis in Regular Model Checking. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 198–213. Springer, Heidelberg (2008)
To, A.W., Libkin, L.: Algorithmic Metatheorems for Decidable LTL Model Checking over Infinite Systems. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 221–236. Springer, Heidelberg (2010)
Rubin, S.: Automata presenting structures: A survey of the finite string case. Bulletin of Symbolic Logic 14, 169–209 (2008)
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Kuske, D., Weidner, T. (2011). Size and Computation of Injective Tree Automatic Presentations. In: Murlak, F., Sankowski, P. (eds) Mathematical Foundations of Computer Science 2011. MFCS 2011. Lecture Notes in Computer Science, vol 6907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22993-0_39
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DOI: https://doi.org/10.1007/978-3-642-22993-0_39
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