Efficient enumeration of weighted tree languages over the tropical semiring

Improved N-Best Extraction with an Evaluation on Language Data

“…The equivalence of the second and the third is shown explicitly in Jonsson (2021). All three have been used in the context of N -best problems: weighted regular tree grammars by May and Knight (2006), weighted tree automata by Björklund, Drewes, and Zechner (2019), and hypergraphs by Huang and Chiang (2005) and Büchse et al (2010). In this paper, we use weighted tree automata.…”

“…In this section, we explain how the algorithm in (Björklund, Drewes, and Zechner 2019) can be made lazier, and hence more efficient, by exploring the search space with respect to transitions rather than states. From here on, let M = (Q, Σ, R, q f ) be a wta with m transition rules, n states, and a maximum rank of r among the symbols in Σ.…”

“…We first summarize the approach of Björklund, Drewes, and Zechner (2019). The algorithm maintains two data structures: an initially empty set T that collects all processed trees, and a priority queue K of trees in Σ(T ) that will be examined next.…”

“…In previous work, Björklund, Drewes, and Zechner (2019) generalized an N -best algorithm by Mohri and Riley (2002) from strings to trees, resulting in the algorithm BEST TREES V.1. Intuitively, the algorithm performs a lazy implicit determinisation and uses a priority queue to output N best trees in the right order.…”

“…The queue K τ of transition τ contains trees which are instantiations of τ , that is, trees with a run that applies τ at the root. This makes it possible to improve the strategy to prune the queue that was used by Björklund, Drewes, and Zechner (2019), and avoiding pruning altogether. The intuition is simple: To assemble N distinct output trees, at most N instantiations of any one transition may be needed.…”