We introduce new classes of weighted automata on words. Equipped with pebbles and a two-way mechanism, they go beyond the class of recognizable formal power series, but capture a weighted version of first-order logic with bounded transitive closure. In contrast to previous work, this logic allows for unrestricted use of universal quantification. Our main result states that pebble weighted automata, nested weighted automata, and this weighted logic are expressively equivalent. We also give new logical characterizations of the recognizable series. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Bollig, B., Gastin, P., Monmege, B., & Zeitoun, M. (2010). Pebble weighted automata and transitive closure logics. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6199 LNCS, pp. 587–598). https://doi.org/10.1007/978-3-642-14162-1_49
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