Abstract
We define regular expressions for unranked trees (actually, ordered sequences of unranked trees, called forests). These are compared to existing regular expressions for trees. On the negative side, our expressions have complementation, and do not define all regular languages. On the positive side, our expressions do not use variables, and have a syntax very similar to that of regular expressions for word languages.
We examine the expressive power of these expressions, especially from a logical point of view. The class of languages defined corresponds to a form of chain logic [5,6]. Furthermore, the star-free expressions coincide with first-order logic. Finally, we show that a concatenation hierarchy inside the expressions corresponds to the quantifier prefix hierarchy for first-order logic, generalizing a result of Thomas.
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References
Bojańczyk, M., Walukiewicz, I.: Forest algebras (unpublished manuscript), http://hal.archives-ouvertes.fr/ccsd-00105796
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© 2007 Springer-Verlag Berlin Heidelberg
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Bojańczyk, M. (2007). Forest Expressions. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_14
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DOI: https://doi.org/10.1007/978-3-540-74915-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74914-1
Online ISBN: 978-3-540-74915-8
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