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

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8977)

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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References

  1. 1.
    Björklund, J., Drewes, F., Zechner, N.: An efficient best-trees algorithm for weighted tree automata over the tropical semiring. Report UMINF 14.22, Umeå University (2014)Google Scholar
  2. 2.
    Borchardt, B.: A pumping lemma and decidability problems for recognizable tree series. Acta Cybernetica 16, 509–544 (2004)MATHMathSciNetGoogle Scholar
  3. 3.
    Collins, M.: Discriminative reranking for natural language parsing. In: Computational Linguistics, pp. 175–182. Morgan Kaufmann (2000)Google Scholar
  4. 4.
    Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata. Springer (2009)Google Scholar
  5. 5.
    Eppstein, D.: Finding the \(k\) shortest paths. SIAM J. Computing 28(2), 652–673 (1998)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Huang, L., Chiang, D.: Better \(k\)-best parsing. In: Proceedings of the Conference on Parsing Technology 2005, pp. 53–64. Association for Computational Linguistics (2005)Google Scholar
  7. 7.
    Knuth, D.E.: A generalization of Dijkstra’s algorithm. Information Processing Letters 6, 1–5 (1977)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Mohri, M., Riley, M.: An efficient algorithm for the \(n\)-best-strings problem. In: Proceedings of the Conference on Spoken Language Processing (2002)Google Scholar
  9. 9.
    Shen, L.: Discriminative reranking for machine translation. In: Proceedings of HLT-NAACL 2004, pp. 177–184 (2004)Google Scholar

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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