Abstract
Nested Pushdown Trees are unfoldings of pushdown graphs with an additional jump-relation. These graphs are closely related to collapsible pushdown graphs. They enjoy decidable μ-calculus model checking while monadic second-order logic is undecidable on this class. We show that nested pushdown trees are tree-automatic structures, whence first-order model checking is decidable. Furthermore, we prove that it is in 2-EXPSPACE using pumping arguments on runs of pushdown systems. For these arguments we also develop a Gaifman style argument for graphs of small diameter.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alur, R., Chaudhuri, S., Madhusudan, P.: Languages of nested trees. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 329–342. Springer, Heidelberg (2006)
Blumensath, A.: Automatic structures. Diploma thesis, RWTH Aachen (1999)
Blumensath, A.: On the structure of graphs in the caucal hierarchy. Theor. Comput. Sci. 400(1-3), 19–45 (2008)
Blumensath, A., Grädel, E.: Automatic structures. In: Proc. 15th IEEE Symp. on Logic in Computer Science, pp. 51–62. IEEE Computer Society Press, Los Alamitos (2000)
Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981)
Grädel, E.: Finite model theory and descriptive complexity. In: Finite Model Theory and Its Applications, pp. 125–230. Springer, Heidelberg (2007)
Hague, M., Murawski, A.S., Ong, C.-H.L., Serre, O.: Collapsible pushdown automata and recursion schemes. In: LICS 2008: Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science, pp. 452–461 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kartzow, A. (2009). FO Model Checking on Nested Pushdown Trees. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_39
Download citation
DOI: https://doi.org/10.1007/978-3-642-03816-7_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03815-0
Online ISBN: 978-3-642-03816-7
eBook Packages: Computer ScienceComputer Science (R0)