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Weighted Nested Word Automata and Logics over Strong Bimonoids

  • Manfred Droste
  • Bundit Pibaljommee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7381)

Abstract

Nested words have been introduced by Alur and Madhusudan as a model for e.g. recursive programs or XML documents and have received much recent interest. In this paper, we investigate a quantitative automaton model and a quantitative logic for nested words. The behavior resp. the semantics map nested words to weights taken from a strong bimonoid. Strong bimonoids can be viewed as semirings without requiring the distributivity assumption which was essential in the classical theory of formal power series; strong bimonoids include e.g. all bounded lattices and many other structures from multi-valued logics. Our main results show that weighted nested word automata and suitable weighted MSO logics are expressively equivalent. This extends the classical Büchi-Elgot result from words to a weighted setting for nested words.

Keywords

Formal Power Series Quantum Logic Boolean Formula Complement Function Weighted Logic 
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 2012

Authors and Affiliations

  • Manfred Droste
    • 1
  • Bundit Pibaljommee
    • 2
  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany
  2. 2.Department of Mathematics, Faculty of ScienceKhon Kaen UniversityKhon KaenThailand

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