Abstract
We establish that regularly extended two-way nondeterministic tree automata with unranked alphabets have the same expressive power as regularly extended nondeterministic tree automata with unranked alphabets. We obtain this result by establishing regularly extended versions of a congruence on trees and of a congruence on, so called, views. Our motivation for the study of these tree models is the Extensible Markup Language (XML), a metalanguage for defining document grammars. Such grammars have regular sets of right-hand sides for their productions and tree automata provide an alternative and useful modeling tool for them. In particular, we believe that they provide a useful computational model for what we call caterpillar expressions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. Barrero. Unranked tree languages. Pattern Recognition, 24(1):9–18, 1991.
T. Bray, J.P. Paoli, and C.M. Sperberg-McQueen. Extensible markup language (XML) 1.0. http://www.w3.org/TR/1998/REC-xml-19980210/, February 1998.
A. Brüggemann-Klein and D. Wood. Caterpillars: A context specification technique, 2000. To appear in Markup Languages.
H. Comon, M. Daucher, R. Gilleron, S. Tison, and M. Tommasi. Tree automata techniques and applications, 1998. Available on the Web from l3ux02.univ-lille3.fr in directory tata.
F. Gécseg and M. Steinby. Tree Automata. Akadémiai Kiadó, Budapest, 1984.
F. Gécseg and M. Steinby. Tree languages. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, Volume 3, Beyond Words, pages 1–68. Springer-Verlag, Berlin, Heidelberg, New York, 1997.
ISO 8879: Information processing—Text and office systems—Standard Generalized Markup Language (SGML), October 1986. International Organization for Standardization.
E. Moriya. On two-way tree automata. Information Processing Letters, 50:117–121, 1994.
M. Murata. Forest-regular languages and tree-regular languages. Unpublished manuscript, 1995.
K. Salomaa. Yield-languages of two-way pushdown tree automata. Information Processing Letters, 58:195–199, 1996.
M. Takahashi. Generalization of regular sets and their application to a study of context-free languages. Information and Control, 27(1):1–36, January 1975.
J.W. Thatcher. Characterizing derivation trees of context-free grammars through a generalization of finite automata theory. Journal of Computer and System Sciences, 1:317–322, 1967.
J.W. Thatcher. A further generalization of finite automata. Technical Report RC 1846, IBM Thomas J. Watson Research Center, Yorktown Heights, New York, 1967.
J.W. Thatcher. There’s a lot more to finite automata theory than you would have thought. Technical Report RC 2852 (#13407), IBM Thomas J. Watson Research Center, Yorktown Heights, New York, 1970.
J.W. Thatcher and J.B. Wright. Abstract 65T-469. Notices of the American Mathematical Society, 12:820, 1965.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brüggemann-Klein, A., Wood, D. (2001). Regularly Extended Two-Way Nondeterministic Tree Automata. In: Yu, S., Păun, A. (eds) Implementation and Application of Automata. CIAA 2000. Lecture Notes in Computer Science, vol 2088. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44674-5_4
Download citation
DOI: https://doi.org/10.1007/3-540-44674-5_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42491-8
Online ISBN: 978-3-540-44674-3
eBook Packages: Springer Book Archive