Abstract
To combine tree languages with term rewriting, we introduce a new class of tree languages, that both extends regular languages and restricts context-free languages, and that is closed under intersection (unlike context-free languages). To do it, we combine the concept of visibly pushdown language, with top-down pushdown tree automata, and we get the visibly pushdown tree automata. Then, we use them to express the sets of descendants for a sub-class of growing term rewrite systems, and thanks to closure under intersection, we get that joinability and (restricted) unifiability are decidable.
This is a preview of subscription content, log in via an institution to check access.
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
Alur, R., Chaudhuri, S., Madhusudan, P.: Languages of Nested Trees. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, Springer, Heidelberg (2006)
Alur, R., Madhusudan, P.: Visibly Pushdown Languages. In: Proc. 36th ACM Symposium on Theory of Computing (STOC 2004), pp. 202–211. ACM Press, New York (2004)
Comon, H., Dauchet, M., Gilleron, R., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (TATA), http://www.grappa.univ-lille3.fr/tata
Genet, T., Klay, F.: Rewriting for cryptographic protocol verification. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, Springer, Heidelberg (2000)
Gouranton, V., Réty, P., Seidl, H.: Synchronized Tree Languages Revisited and New Applications. In: Honsell, F., Miculan, M. (eds.) ETAPS 2001 and FOSSACS 2001. LNCS, vol. 2030, Springer, Heidelberg (2001)
Guessarian, I.: Pushdown Tree Automata. Mathematical Systems Theory 4(16), 237–263 (1983)
Hermann, M., Galbavý, R.: Unification of Infinite Sets of Terms Schematized by Primal Grammars. Theoretical Computer Science, 176 (1997)
Jacquemard, F.: Decidable approximations of term rewrite systems. In: Ganzinger, H. (ed.) RTA 1996. LNCS, vol. 1103, pp. 362–376. Springer, Heidelberg (1996)
Limet, S., Réty, P.: A New Result about the Decidability of the Existential One-Step Rewriting Theory. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, Springer, Heidelberg (1999)
Limet, S., Salzer, G.: Proving properties of term rewrite systems via logic programs. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 170–184. Springer, Heidelberg (2004)
Limet, S., Salzer, G.: Manipulating tree tuple languages by transforming logic programs. In: Dahn, I., Vigneron, L. (eds.) Electronic Notes in Theoretical Computer Science, vol. 86, Elsevier, Amsterdam (2003)
Lugiez, D., Schnoebelen, P.: The Regular Viewpoint on PA-Processes. Theoretical Computer Science (2000)
Nagaya, T., Toyama, Y.: Decidability for Left-Linear Growing Term Rewriting Systems. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, Springer, Heidelberg (1999)
Raoult, J.C.: Rational Tree Relations. Bulletin of the Belgian Mathematical Society Simon Stevin 4, 149–176 (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chabin, J., Réty, P. (2007). Visibly Pushdown Languages and Term Rewriting. In: Konev, B., Wolter, F. (eds) Frontiers of Combining Systems. FroCoS 2007. Lecture Notes in Computer Science(), vol 4720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74621-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-74621-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74620-1
Online ISBN: 978-3-540-74621-8
eBook Packages: Computer ScienceComputer Science (R0)