Abstract
Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative context-free languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schützenberger Theorem for such quantitative context-free languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative context-free languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings.
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Droste, M., Vogler, H. (2013). The Chomsky-Schützenberger Theorem for Quantitative Context-Free Languages. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_19
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DOI: https://doi.org/10.1007/978-3-642-38771-5_19
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