Abstract
Tree automata with one memory have been introduced in 2001. They generalize both pushdown (word) automata and the tree automata with constraints of equality between brothers of Bogaert and Tison. Though it has a decidable emptiness problem, the main weakness of this model is its lack of good closure properties.
We propose a generalization of the visibly pushdown automata of Alur and Madhusudan to a family of tree recognizers which carry along their (bottom-up) computation an auxiliary unbounded memory with a tree structure (instead of a symbol stack). In other words, these recognizers, called visibly Tree Automata with Memory (VTAM) define a subclass of tree automata with one memory enjoying Boolean closure properties. We show in particular that they can be determinized and the problems like emptiness, inclusion and universality are decidable for VTAM. Moreover, we propose an extension of VTAM whose transitions may be constrained by structural equality and disequality tests between memories, and show that this extension preserves the good closure and decidability properties.
Chapter PDF
Similar content being viewed by others
References
Alur, R., Chaudhuri, S., Madhusudan, P.: Visibly pushdown tree languages (2006), Available on http://www.cis.upenn.edu/~swarat/pubs/vptl.ps
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Babai, L. (ed.) Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC 2004), pp. 202–211. ACM Press, New York (2004)
Bogaert, B., Tison, S.: Equality and Disequality Constraints on Direct Subterms in Tree Automata. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 161–171. Springer, Heidelberg (1992)
Comon, H., Cortier, V.: Tree automata with one memory, set constraints and cryptographic protocols. Theoretical Computer Science 331(1), 143–214 (2005)
Comon, H., et al.: Tree Automata Techniques and Applications (1997), http://www.grappa.univ-lille3.fr/tata
Comon, H., Jacquemard, F.: Ground reducibility is exptime-complete. Information and Computation 187(1), 123–153 (2003)
Comon-Lundh, H., Jacquemard, F., Perrin, N.: Tree automata with memory, visibility and structural constraints. Technical Report LSV-07-01, Laboratoire Spécification et Vérification (Jan. 2007)
Coquidé, J.-L., et al.: Bottom-up tree pushdown automata: classification and connection with rewrite systems. Theoretical Computer Science 127(1), 69–98 (1994)
Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: Handbook of Theoretical Computer Science, vol. B, pp. 243–320. Elsevier, Amsterdam (1990)
Guessarian, I.: Pushdown tree automata. Theory of Computing Systems 16(1), 237–263 (1983)
Habermehl, P., Iosif, R., Vojnar, T.: Automata-based verification of programs with tree updates. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006 and ETAPS 2006. LNCS, vol. 3920, Springer, Heidelberg (2006)
Jensen, T., Métayer, D.L., Thorn, T.: Verification of control flow based security policies. In: Proceedings of the IEEE Symposium on Research in Security and Privacy, pp. 89–103. IEEE Computer Society Press, Los Alamitos (1999)
Kapur, D.: Constructors can be Partial Too. In: Automated reasoning and its applications: essays in honor of Larry Wos, MIT Press, Cambridge (1997)
Misra, J.: Powerlist: A structure for parallel recursion. ACM Transactions on Programming Languages and Systems 16(6), 1737–1767 (1994)
Schimpf, K.M., Gallier, J.: Tree pushdown automata. Journal of Computer and System Sciences 30(1), 25–40 (1985)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Comon-Lundh, H., Jacquemard, F., Perrin, N. (2007). Tree Automata with Memory, Visibility and Structural Constraints. In: Seidl, H. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2007. Lecture Notes in Computer Science, vol 4423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71389-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-71389-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71388-3
Online ISBN: 978-3-540-71389-0
eBook Packages: Computer ScienceComputer Science (R0)