Abstract
Tree Walking Automata (TWA) have lately received renewed interest thanks to their tight connection to XML. This paper introduces the notion of tree overloops, which is closely related to tree loops, and investigates the use of both for the following common operations on TWA: testing membership, transformation into a Bottom-Up Tree Automaton (BUTA), and testing emptiness. Notably, we argue that transformation into a BUTA is slightly less straightforward than was assumed, show that using overloops yields much smaller BUTA in the deterministic case, and provide a polynomial over-approximation of this construction which detects emptiness with surprising accuracy against randomly generated TWA.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho, A., Ullman, J.: Translations on a context free grammar. Information and Control 19(5), 439–475 (1969)
Bojańczyk, M.: 1-bounded TWA cannot be determinized. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 62–73. Springer, Heidelberg (2003)
Bojańczyk, M.: Tree-walking automata. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 1–2. Springer, Heidelberg (2008), http://www.mimuw.edu.pl/~bojan/papers/twasurvey.pdf
Bojańczyk, M., Colcombet, T.: Tree-walking automata cannot be determinized. Theoretical Computer Science 350(2-3), 164–173 (2006)
Bojańczyk, M., Colcombet, T.: Tree-walking automata do not recognize all regular languages. In: STOC 2005, pp. 234–243. ACM Press, New York (2005)
ten Cate, B., Segoufin, L.: Transitive closure logic, nested tree walking automata, and XPath. J. ACM 57(3), 251–260 (2010)
Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007)
Cosmadakis, S., Gaifman, H., Kanellakis, P., Vardi, M.: Decidable optimization problems for database logic programs. In: STOC 1988, pp. 477–490. ACM Press, New York (1988)
Heam, P., Hugot, V., Kouchnarenko, O.: Random Generation of Positive TAGEDs wrt. the Emptiness Problem. Tech. Rep. RR-7441, INRIA (November 2010)
Héam, P.-C., Nicaud, C., Schmitz, S.: Random generation of deterministic tree (Walking) automata. In: Maneth, S. (ed.) CIAA 2009. LNCS, vol. 5642, pp. 115–124. Springer, Heidelberg (2009)
Knuth, D.: Semantics of context-free languages: Correction. Theory of Computing Systems 5(2), 95–96 (1971)
Samuelides, M.: Automates d’arbres à jetons. Ph.D. thesis, Université Paris-Diderot - Paris VII (December 2007), http://tel.archives-ouvertes.fr/tel-00255024/en/
Segoufin, L., Vianu, V.: Validating Streaming XML Documents. In: Popa, L. (ed.) PODS, pp. 53–64. ACM, New York (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Héam, PC., Hugot, V., Kouchnarenko, O. (2011). Loops and Overloops for Tree Walking Automata. In: Bouchou-Markhoff, B., Caron, P., Champarnaud, JM., Maurel, D. (eds) Implementation and Application of Automata. CIAA 2011. Lecture Notes in Computer Science, vol 6807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22256-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-22256-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22255-9
Online ISBN: 978-3-642-22256-6
eBook Packages: Computer ScienceComputer Science (R0)