Weighted Specifications over Nested Words

  • Benedikt Bollig
  • Paul Gastin
  • Benjamin Monmege
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7794)

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.

Keywords

Temporal Logic Regular Expression Zero Divisor Tree Automaton Recursive Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Benedikt Bollig
    • 1
  • Paul Gastin
    • 1
  • Benjamin Monmege
    • 1
  1. 1.LSV, ENS Cachan, CNRS & InriaFrance

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