Abstract
A formula from monadic second-order (MSO) logic can be used to specify a binary relation on the set of nodes of a tree. It is proved that, equivalently, such a relation can be computed by a finite-state tree-walking automaton, provided the automaton can test MSO properties of the nodes of the tree. For graphs, if a binary relation on the nodes of a graph can be computed by a finite-state graph-walking automaton, then it can be specified by an MSO formula, but, in general, not vice versa.
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© 1997 Springer-Verlag Berlin Heidelberg
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Bloem, R., Engelfriet, J. (1997). Monadic second order logic and node relations on graphs and trees. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds) Structures in Logic and Computer Science. Lecture Notes in Computer Science, vol 1261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63246-8_9
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DOI: https://doi.org/10.1007/3-540-63246-8_9
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