Logical Characterization of Weighted Pebble Walking Automata

Benedikt Bollig (1, 2) , Paul Gastin (1, 2) , Benjamin Monmege (3) , Marc Zeitoun (4)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 MEXICO - Modeling and Exploitation of Interaction and Concurrency
3 ULB - Département d'Informatique [Bruxelles]
4 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Weighted automata are a conservative quantitative extension of finite automata that enjoys applications, e.g., in language processing and speech recognition. Their expressive power, however, appears to be limited, especially when they are applied to more general structures than words, such as graphs. To address this drawback, weighted automata have recently been generalized to weighted pebble walking automata, which proved useful as a tool for the specification and evaluation of quantitative properties over words and nested words. In this paper, we establish the expressive power of weighted pebble walking automata in terms of transitive closure logic, lifting a similar result by Engelfriet and Hoogeboom from the Boolean case to a quantitative setting. This result applies to a general class of graphs that subsumes all the aforementioned classes.

Domaines: Théorie et langage formel [cs.FL]; Logique en informatique [cs.LO]

Benedikt Bollig, Paul Gastin, Benjamin Monmege, Marc Zeitoun. Logical Characterization of Weighted Pebble Walking Automata. CSL-LICS '14, Jul 2014, Vienna, Austria. ⟨10.1145/2603088.2603118⟩. ⟨hal-01006125⟩