Nested pebbles and transitive closure

Authors:
Joost Engelfriet;Hendrik Jan Hoogeboom
Affiliations:
Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands;Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands
Venue:
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Year:
2006

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Abstract

First-order logic with k-ary deterministic transitive closure has the same power as two-way k-head deterministic automata that use a finite set of nested pebbles. This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes.