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
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 \(M\).