Abstract
This paper studies several formalisms to specify quantitative properties of finite nested words (or equivalently finite unranked trees). These can be used for XML documents or recursive programs: for instance, counting how often a given entry occurs in an XML document, or computing the memory required for a recursive program execution. Our main interest is to translate these properties, as efficiently as possible, into an automaton, and to use this computational device to decide problems related to the properties (e.g., emptiness, model checking, simulation) or to compute the value of a quantitative specification over a given nested word. The specification formalisms are weighted regular expressions (with forward and backward moves following linear edges or call-return edges), weighted first-order logic, and weighted temporal logics. We introduce weighted automata walking in nested words, possibly dropping/lifting (reusable) pebbles during the traversal. We prove that the evaluation problem for such automata can be done very efficiently if the number of pebble names is small, and we also consider the emptiness problem.
This work was partially supported by LIA INFORMEL.
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Bollig, B., Gastin, P., Monmege, B. (2013). Weighted Specifications over Nested Words. In: Pfenning, F. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2013. Lecture Notes in Computer Science, vol 7794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37075-5_25
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