An Efficient Best-Trees Algorithm for Weighted Tree Automata over the Tropical Semiring

  • Johanna Björklund
  • Frank Drewes
  • Niklas Zechner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8977)


We generalise a search algorithm by Mohri and Riley from strings to trees. The original algorithm takes as input a weighted automaton \(M\) over the tropical semiring, together with an integer \(N\), and outputs \(N\) strings of minimal weight with respect to \(M\). In our setting, \(M\) defines a weighted tree language, again over the tropical semiring, and the output is a set of \(N\) trees with minimal weight. We prove that the algorithm is correct, and that its time complexity is a low polynomial in \(N\) and the relevant size parameters of \(M\).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Johanna Björklund
    • 1
  • Frank Drewes
    • 1
  • Niklas Zechner
    • 1
  1. 1.Department of Computing ScienceUmeå UniversityUmeåSweden

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