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

Conference paper

DOI: 10.1007/978-3-319-15579-1_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8977)
Cite this paper as:
Björklund J., Drewes F., Zechner N. (2015) An Efficient Best-Trees Algorithm for Weighted Tree Automata over the Tropical Semiring. In: Dediu AH., Formenti E., Martín-Vide C., Truthe B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science, vol 8977. Springer, Cham

Abstract

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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