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Determinization of weighted tree automata using factorizations
 PRESENTATION AT 8TH INT. WORKSHOP FINITESTATE METHODS AND NATURAL LANGUAGE PROCESSING
, 2009
"... We present a determinization construction for weighted tree automata using factorizations. Among others, this result subsumes a previous result for determinization of weighted string automata using factorizations (Kirsten and Mäurer, 2005) and two previous results for weighted tree automata, one of ..."
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We present a determinization construction for weighted tree automata using factorizations. Among others, this result subsumes a previous result for determinization of weighted string automata using factorizations (Kirsten and Mäurer, 2005) and two previous results for weighted tree automata, one of them not using factorizations (Borchardt, 2004) and one of them restricted to nonrecursive automata over the nonnegative reals (May and Knight, 2006).
Pushing for weighted tree automata
 IN PROC. 36TH INT. SYMP. MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE, VOLUME 6907 OF LNCS
, 2011
"... Explicit pushing for weighted tree automata over semifields is introduced. A careful selection of the pushing weights allows a normalization of bottomup deterministic weighted tree automata. Automata in the obtained normal form can be minimized by a simple transformation into an unweighted automat ..."
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Explicit pushing for weighted tree automata over semifields is introduced. A careful selection of the pushing weights allows a normalization of bottomup deterministic weighted tree automata. Automata in the obtained normal form can be minimized by a simple transformation into an unweighted automaton followed by unweighted minimization. This generalizes results of Mohri and Eisner for deterministic weighted string automata to the tree case. Moreover, the new strategy can also be used to test equivalence of two bottomup deterministic weighted tree automata M1 and M2 in time O(M  logQ), where M = M1 + M2 and Q is the sum of the number of states of M1 and M2. This improves the previously best running time O(M1 · M2).
A Backward and a Forward Simulation for Weighted Tree Automata ⋆
"... Abstract. Two types of simulations for weighted tree automata (wta) are considered. Wta process trees as input and assign a weight to them. The weights are taken from a semiring. The two considered types of simulations work for wta over additively idempotent, commutative semirings and can be used to ..."
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Abstract. Two types of simulations for weighted tree automata (wta) are considered. Wta process trees as input and assign a weight to them. The weights are taken from a semiring. The two considered types of simulations work for wta over additively idempotent, commutative semirings and can be used to reduce the size of wta while preserving their semantics. Such reductions are an important tool in automata toolkits. 1
HyperMinimization for Deterministic Tree Automata
, 2012
"... Hyperminimization aims to reduce the size of the representation of a language beyond the limits imposed by classical minimization. To this end, the hyperminimal representation can represent a language that has a finite difference to the original language. The first hyperminimization algorithm is ..."
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Hyperminimization aims to reduce the size of the representation of a language beyond the limits imposed by classical minimization. To this end, the hyperminimal representation can represent a language that has a finite difference to the original language. The first hyperminimization algorithm is presented for (bottomup) deterministic tree automata, which represent the recognizable tree languages. It runs in time O(ℓmn), where ℓ is the maximal rank of the input symbols, m is the number of transitions, and n is the number of states of the input tree automaton.
Minimizing Weighted Tree Grammars using Simulation
, 2009
"... Weighted tree grammars (for short: WTG) are an extension of weighted contextfree grammars that generate trees instead of strings. They can be used in natural language parsing to directly generate the parse tree of a sentence or to encode the set of all parse trees of a sentence. Two types of simul ..."
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Weighted tree grammars (for short: WTG) are an extension of weighted contextfree grammars that generate trees instead of strings. They can be used in natural language parsing to directly generate the parse tree of a sentence or to encode the set of all parse trees of a sentence. Two types of simulations for WTG over idempotent, commutative semirings are introduced. They generalize the existing notions of simulation and bisimulation for WTG. Both simulations can be used to reduce the size of WTG while preserving the semantics, and are thus an important tool in toolkits. Since the new notions are more general than the existing ones, they yield the best reduction rates achievable by all minimization procedures that rely on simulation or bisimulation. However, the existing notions might allow faster minimization.