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Bisimulation Minimisation of Weighted Automata on Unranked Trees
, 2008
"... Two examples of automatatheoretic models for the validation of xml documents against userde ned schema are the stepwise unranked tree automaton (suta) and the parallel unranked tree automaton (puta). By adding a weight, taken from some semiring, to every transition we generalise these two qualitat ..."
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Cited by 4 (1 self)
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Two examples of automatatheoretic models for the validation of xml documents against userde ned schema are the stepwise unranked tree automaton (suta) and the parallel unranked tree automaton (puta). By adding a weight, taken from some semiring, to every transition we generalise these two qualitative automata models to quantitative models, thereby obtaining weighted stepwise unranked tree automata (wsuta) and weighted parallel unranked tree automata (wputa); the qualitative automata models are reobtained by choosing the Boolean semiring. We deal with the minimisation problem of wsuta and wputa by using (forward and backward) bisimulations and we prove the following results: (1) for every wsuta an equivalent forward (resp. backward) bisimulation minimal wsuta can be computed in time O(mn) where n is the number of states and m is the number of transitions of the given wsuta; (2) the same result is proved for wputa instead of wsuta; (3) if the semiring is additive cancellative or the Boolean semiring, then the bound can be improved to O(m log n) for both wsuta and wputa; (4) for every deterministic puta we can compute a minimal equivalent deterministic puta in time O(m log n); (5) the automata models wsuta, wputa, and weighted unranked tree automaton have the same computational power.
A Uniform (Bi)SimulationBased Framework for Reducing Tree Automata
, 2008
"... In this paper, we address the problem of reducing the size of nondeterministic (bottomup) tree automata. We propose a uniform framework that allows for combining various upward and downward bisimulation and simulation relations in order to obtain a languagepreserving combined relation suitable for ..."
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Cited by 3 (2 self)
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In this paper, we address the problem of reducing the size of nondeterministic (bottomup) tree automata. We propose a uniform framework that allows for combining various upward and downward bisimulation and simulation relations in order to obtain a languagepreserving combined relation suitable for reducing tree automata without a need to determinise them. The framework generalises and extends several previous works and provides a broad spectrum of different relations yielding a possibility of a fine choice between the amount of reduction and the computational demands. We, moreover, provide a significantly improved way of computing the various combined (bi)simulation relations. We analyse properties of the considered relations both theoretically as well as through a series of experiments.
2011. Pushing for weighted tree automata
 In Proc. 36th Int. Symp. Mathematical Foundations of Computer Science, volume 6907 of LNCS
"... Abstract. 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 unweighte ..."
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Cited by 2 (2 self)
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Abstract. 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). 1
The Category of Simulations for Weighted Tree Automata ⋆
"... Abstract. Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noether ..."
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Cited by 1 (0 self)
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Abstract. Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noetherian semirings, semiring of natural numbers) that all equivalent wta M and N can be joined by a finite chain of simulations. More precisely, in all mentioned cases there is a single wta that simulates both M and N. Those results immediately yield decidability of equivalence provided that the semiring is finitely (and effectively) presented. 1
Minimizing Weighted Tree Grammars using Simulation ⋆
"... Abstract. 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 ..."
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Abstract. 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. 1
Simulations of Weighted Tree Automata
"... Abstract. Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noether ..."
Abstract
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Abstract. Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noetherian semirings, semiring of natural numbers) that all equivalent wta M and N can be joined by a finite chain of simulations. More precisely, in all mentioned cases there is a single wta that simulates both M and N. Those results immediately yield decidability of equivalence provided that the semiring is finitely (and effectively) presented. 1