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11
Bisimulation Minimisation for Weighted Tree Automata
, 2007
"... We generalise existing forward and backward bisimulation minimisation algorithms for tree automata to weighted tree automata. The obtained algorithms work for all semirings and retain the time complexity of their unweighted variants for all additively cancellative semirings. On all other semirings t ..."
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Cited by 8 (6 self)
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We generalise existing forward and backward bisimulation minimisation algorithms for tree automata to weighted tree automata. The obtained algorithms work for all semirings and retain the time complexity of their unweighted variants for all additively cancellative semirings. On all other semirings the time complexity is slightly higher (linear instead of logarithmic in the number of states). We discuss implementations of these algorithms on a typical task in natural language processing.
Computing Simulations over Tree Automata: Efficient Techniques for Reducing Tree Automata
 In Proc. of TACAS’08, LNCS
, 2008
"... Abstract. We address the problem of computing simulation relations over tree automata. In particular, we consider downward and upward simulations on tree automata, which are, loosely speaking, analogous to forward and backward relations over word automata. We provide simple and efficient algorithms ..."
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Cited by 5 (3 self)
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Abstract. We address the problem of computing simulation relations over tree automata. In particular, we consider downward and upward simulations on tree automata, which are, loosely speaking, analogous to forward and backward relations over word automata. We provide simple and efficient algorithms for computing these relations based on a reduction to the problem of computing simulations on labelled transition systems. Furthermore, we show that downward and upward relations can be combined to get relations compatible with the tree language equivalence, which can subsequently be used for an efficient size reduction of nondeterministic tree automata. This is of a very high interest, for instance, for symbolic verification methods such as regular model checking, which use tree automata to represent infinite sets of reachable configurations. We provide experimental results showing the efficiency of our algorithms on examples of tree automata taken from regular model checking computations. 1
Backward and Forward Bisimulation Minimization of Tree Automata
, 2008
"... We improve on an existing [P.A. Abdulla, J. Högberg, L. Kaati. Bisimulation Minimization of ..."
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Cited by 5 (4 self)
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We improve on an existing [P.A. Abdulla, J. Högberg, L. Kaati. Bisimulation Minimization of
Minimizing Deterministic Weighted Tree Automata
, 2008
"... The problem of efficiently minimizing deterministic weighted tree automata (wta) is investigated. Such automata have found promising applications as language models in Natural Language Processing. A polynomialtime algorithm is presented that given a deterministic wta over a commutative semifield, o ..."
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Cited by 5 (4 self)
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The problem of efficiently minimizing deterministic weighted tree automata (wta) is investigated. Such automata have found promising applications as language models in Natural Language Processing. A polynomialtime algorithm is presented that given a deterministic wta over a commutative semifield, of which all operations including the computation of the inverses are polynomial, constructs an equivalent minimal (with respect to the number of states) deterministic and total wta. If the semifield operations can be performed in constant time, then the algorithm runs in time O(rmn 4) where r is the maximal rank of the input symbols, m is the number of transitions, and n is the number of states of the input wta.
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.
Composed Bisimulation for Tree Automata
, 2008
"... We address the problem of reducing the size of (nondeterministic, bottomup) tree automata (TA) using suitable, languagepreserving equivalences on the states of the automata. In particular, we propose the socalled composed bisimulation equivalence as a new language preserving equivalence. A compos ..."
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Cited by 2 (0 self)
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We address the problem of reducing the size of (nondeterministic, bottomup) tree automata (TA) using suitable, languagepreserving equivalences on the states of the automata. In particular, we propose the socalled composed bisimulation equivalence as a new language preserving equivalence. A composed bisimulation equivalence is defined in terms of two different relations, namely the upward and downward bisimulation equivalence. We provide simple and efficient algorithms for computing these relations. The notion of composed bisimulation equivalence is motivated by an attempt to obtain an equivalence that can provide better reductions than what currently known bisimulationbased approaches can offer, but which is not significantly more difficult to compute (and hence stays below the computational requirements of simulationbased reductions). The experimental results we present in the paper show that our composed bisimulation equivalence meets such requirements, and hence provides users of TA with a finer way to resolve the tradeoff between the available degree of reduction and its cost.
Abstract Regular Tree Model Checking with Nondeterministic Automata
, 2011
"... Abstract regular tree model checking is an infinite state system verification method that is based on representing possibly infinite sets of states by tree automata. The method was originally defined over deterministic tree automata, involving expensive determinisation steps many times within a sing ..."
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Abstract regular tree model checking is an infinite state system verification method that is based on representing possibly infinite sets of states by tree automata. The method was originally defined over deterministic tree automata, involving expensive determinisation steps many times within a single verification run, which significantly limits scalability of the method. To avoid determinisation, we redesign the method on top of nondeterministic tree automata. For this, we develop needed efficient methods for reducing size and checking language inclusion of nondeterministic tree automata. Our experimental results confirm that the version of abstract regular tree model checking based on nondeterministic automata performs much better than the original deterministic automatabased version.
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.