Language and Automata Theory and Applications

Volume 8977 of the series Lecture Notes in Computer Science pp 97-108


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

  • Johanna BjörklundAffiliated withDepartment of Computing Science, Umeå University
  • , Frank DrewesAffiliated withDepartment of Computing Science, Umeå University Email author 
  • , Niklas ZechnerAffiliated withDepartment of Computing Science, Umeå University

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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 \(M\).