Abstract
Classical verification often uses abstraction when dealing with data. On the other hand, dynamic XML-based applications have become pervasive, for instance with the ever growing importance of web services. We define here Tree Pattern Rewriting Systems (TPRS) as an abstract model of dynamic XML-based documents. TPRS systems generate infinite transition systems, where states are unranked and unordered trees (hence possibly modeling XML documents). Their guarded transition rules are described by means of tree patterns. Our main result is that given a TPRS system \((T,{\mathcal R})\), a tree pattern P and some integer k such that any reachable document from T has depth at most k, it is decidable (albeit of non elementary complexity) whether some tree matching P is reachable from T.
Work supported by ANR DocFlow, ANR DOTS and CREATE ACTIVEDOC.
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
Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.-K.: General decidability theorems for infinite-state systems. In: LICS 1996, pp. 313–321. IEEE Comp. Soc, Los Alamitos (1996)
Abiteboul, S., Benjelloun, O., Milo, T.: Positive Active XML. In: PODS 2004, pp. 35–45. ACM, New York (2004)
Abiteboul, S., Segoufin, L., Vianu, V.: Analysis of Active XML Services. In: PODS 2008. ACM Press, New York (to appear, 2008)
Active XML, http://www.activexml.net/
Chambart, P., Schnoebelen, P.: The Ordinal Recursive Complexity of Lossy Channel Systems. In: LICS 2008, pp. 205–216. IEEE Comp. Soc., Los Alamitos (2008)
R. Diestel. Graph theory (2005), http://www.math.uni-hamburg.de/home/diestel
Dufourd, C., Finkel, A., Schnoebelen, P.: Reset Nets between Decidability and Undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere. Theor. Comput. Sci. 256(1-2), 63–92 (2001)
Genest, B., Muscholl, A., Serre, O., Zeitoun, M.: Tree Pattern Rewrite Systems. Internal report, http://www.crans.org/~genest/GMSZ08.pdf
Dershowitz, N., Plaisted, D.: In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 9, vol. 1. Elsevier, Amsterdam (2001)
Libkin, L.: Logics over unranked trees: an overview. Logical Methods in Computer Science 2(3) (2006)
Löding, C., Spelten, A.: Transition Graphs of Rewriting Systems over Unranked Trees. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 67–77. Springer, Heidelberg (2007)
Neven, F.: Automata, Logic, and XML. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 2–26. Springer, Heidelberg (2002)
Schnoebelen, P.: Verifying Lossy Channel Systems has Nonprimitive Recursive Complexity. Inf. Process. Lett. 83(5), 251–261 (2002)
Walukiewicz, I.: Difficult Configurations—on the Complexity of LTrL. ICALP 1998 26(1), 27–43 (2005); In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 27–43. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Genest, B., Muscholl, A., Serre, O., Zeitoun, M. (2008). Tree Pattern Rewriting Systems. In: Cha, S.(., Choi, JY., Kim, M., Lee, I., Viswanathan, M. (eds) Automated Technology for Verification and Analysis. ATVA 2008. Lecture Notes in Computer Science, vol 5311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88387-6_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-88387-6_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88386-9
Online ISBN: 978-3-540-88387-6
eBook Packages: Computer ScienceComputer Science (R0)