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Weighted Nested Word Automata and Logics over Strong Bimonoids

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Book cover Implementation and Application of Automata (CIAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7381))

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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.

This work has been supported by DFG-NRCT.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, D-04009, Leipzig, Germany

    Manfred Droste

  2. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

    Bundit Pibaljommee

Authors
  1. Manfred Droste
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  2. Bundit Pibaljommee
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Editor information

Editors and Affiliations

  1. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

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Droste, M., Pibaljommee, B. (2012). Weighted Nested Word Automata and Logics over Strong Bimonoids. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-31606-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31605-0

  • Online ISBN: 978-3-642-31606-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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