An Efficient Best-Trees Algorithm for Weighted Tree Automata over the Tropical Semiring
نویسندگان
چکیده
We generalise a search algorithm by Mohri and Riley from strings to trees. The original algorithm takes as input a weighted automaton A over the tropical semiring, together with an integer N , and outputs N strings of minimal weight with respect to A. In our setting, the input automaton 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 , m, n, and r, where m and n are the number of transitions and the number of states of A, respectively, and r is the maximum rank of symbols in the input alphabet. Copyright c © 2014 UMINF 14.22 ISSN 0348-0542
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