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19
Determinization of Finite State Weighted Tree Automata
 J. Autom. Lang. Combin
, 2002
"... We investigate the determinization of nondeterministic bottomup/topdown finite state weighted tree automata over some semiring A and compare the resulting four classes of formal tree series with each other. In fact, we generalize well known theorems on classes of tree languages (cf. [GS84] Chapter ..."
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Cited by 19 (3 self)
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We investigate the determinization of nondeterministic bottomup/topdown finite state weighted tree automata over some semiring A and compare the resulting four classes of formal tree series with each other. In fact, we generalize well known theorems on classes of tree languages (cf. [GS84] Chapter II, Theorems 2.6 and 2.10, Example 2.11), viz. if A is a commutative and locally finite semifield, then (i) nondeterministic bottomup, (ii) deterministic bottomup, and (iii) nondeterministic topdown finite state weighted tree automata are equally powerful. Moreover, if the input alphabet is not trivial, then deterministic topdown finite state weighted tree automata are strictly less powerful than the aforementioned classes.
Max/plus tree automata for termination of term rewriting
 AC
, 2009
"... We use weighted tree automata as certificates for termination of term rewriting systems. The weights are taken from the arctic semiring: natural numbers extended with −∞, with the operations “max ” and “plus”. In order to find and validate these certificates automatically, we restrict their transiti ..."
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Cited by 8 (1 self)
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We use weighted tree automata as certificates for termination of term rewriting systems. The weights are taken from the arctic semiring: natural numbers extended with −∞, with the operations “max ” and “plus”. In order to find and validate these certificates automatically, we restrict their transition functions to be representable by matrix operations in the semiring. The resulting class of weighted tree automata is called pathseparated. This extends the matrix method for term rewriting and the arctic matrix method for string rewriting. In combination with the dependency pair method, this allows for some conceptually simple termination proofs in cases where only much more involved proofs were known before. We further generalize to arctic numbers “below zero”: integers extended with −∞. This allows to treat some termination problems with symbols that require a predecessor semantics. Correctness of this approach has been formally verified in the Coq proof
Parsing algorithms based on tree automata
 IN PROC. IWPT
, 2009
"... We investigate several algorithms related to the parsing problem for weighted automata, under the assumption that the input is a string rather than a tree. This assumption is motivated by several natural language processing applications. We provide algorithms for the computation of parseforests, be ..."
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Cited by 7 (4 self)
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We investigate several algorithms related to the parsing problem for weighted automata, under the assumption that the input is a string rather than a tree. This assumption is motivated by several natural language processing applications. We provide algorithms for the computation of parseforests, best tree probability, inside probability (called partition function), and prefix probability. Our algorithms are obtained by extending to weighted tree automata the BarHillel technique, as defined for contextfree grammars.
Towards Formal Structural Representation of Spoken Language: An Evolving Transformation System (ETS) Approach
, 2005
"... Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new approaches are needed. The motivation ..."
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Cited by 6 (0 self)
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Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new approaches are needed. The motivation behind the undertaken research is an observation that the notion of representation of objects and concepts that once was considered to be central in the early days of pattern recognition, has been largely marginalised by the advent of statistical approaches. As a consequence of a predominantly statistical approach to speech recognition problem, due to the numeric, feature vectorbased, nature of representation, the classes inductively discovered from real data using decisiontheoretic techniques have little meaning outside the statistical framework. This is because decision surfaces or probability distributions are difficult to analyse linguistically. Because of the later limitation it is doubtful that the gap between speech recognition and linguistic research can be bridged by the numeric representations. This thesis investigates an alternative, structural, approach to spoken language representation and categorisa
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 5 (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.
M.: Relevant representations for the inference of rational stochastic tree languages
 In: Grammatical Inference: Algorithms and Applications. Volume 5278 of LNCS. (2008
"... Abstract. Recently, an algorithm DEES was proposed for learning rational stochastic tree languages. Given a sample of trees independently and identically drawn according to a distribution de ned by a rational stochastic language, DEES outputs a linear representation of a rational series which conv ..."
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Abstract. Recently, an algorithm DEES was proposed for learning rational stochastic tree languages. Given a sample of trees independently and identically drawn according to a distribution de ned by a rational stochastic language, DEES outputs a linear representation of a rational series which converges to the target. DEES can then be used to identify in the limit with probability one rational stochastic tree languages. However, when DEES deals with nite samples, it often outputs a rational tree series which does not de ne a stochastic language. Moreover, the linear representation can not be directly used as a generative model. In this paper, we show that any representation of a rational stochastic tree language can be transformed in a reduced normalised representation that can be used to generate trees from the underlying distribution. We also study some properties of consistency for rational stochastic tree languages and discuss their implication for the inference. We nally consider the applicability of DEES to trees built over an unranked alphabet. 1
An extension theorem with an application to formal tree series
 BRICS Report Series
, 2002
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Hasse diagrams for classes of deterministic bottomup treetotreeseries transformations
 THEORET. COMPUT. SCI
, 2006
"... The relationship between classes of treetotreeseries and otreetotreeseries transformations, which are computed by restricted deterministic bottomup weighted tree transducers, is investigated. Essentially, these transducers are deterministic bottomup tree series transducers, except that the ..."
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Cited by 2 (1 self)
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The relationship between classes of treetotreeseries and otreetotreeseries transformations, which are computed by restricted deterministic bottomup weighted tree transducers, is investigated. Essentially, these transducers are deterministic bottomup tree series transducers, except that the former are defined over monoids whereas the latter are defined over semirings and only use the multiplicative monoid thereof. In particular, the common restrictions of nondeletion, linearity, totality, and homomorphism can equivalently be defined for deterministic bottomup weighted tree transducers. Using wellknown results of classical tree transducer theory and also new results on deterministic weighted tree transducers, classes of treetotreeseries and otreetotreeseries transformations computed by restricted deterministic bottomup weighted tree transducers are ordered by set inclusion. More precisely, for every commutative monoid and all sensible combinations of the above mentioned restrictions, the inclusion relation of the classes of treetotreeseries and otreetotreeseries transformations is completely conveyed by means of Hasse diagrams.
Hierarchies of Tree Series Transformations Revisited
, 2006
"... Tree series transformations computed by polynomial topdown and bottomup tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutativ ..."
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Cited by 2 (2 self)
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Tree series transformations computed by polynomial topdown and bottomup tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutative izzsemirings (izz abbreviates idempotent, zerosum and zerodivisor free) is generalized to arbitrary positive (i. e., zerosum and zerodivisor free) commutative semirings. The latter class of semirings includes prominent examples such as the natural numbers semiring and the least common multiple semiring, which are not members of the former class.
A Kleene Theorem for Weighted Tree Automata over Distributive Multioperator Monoids
, 2007
"... Abstract: Kleene's theorem on the equivalence of recognizability and rationality for formal tree series over distributive multioperator monoids is proved. As a consequence of this, Kleene's theorem for weighted tree automata over arbitrary, i.e., not necessarily commutative, semirings is d ..."
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Abstract: Kleene's theorem on the equivalence of recognizability and rationality for formal tree series over distributive multioperator monoids is proved. As a consequence of this, Kleene's theorem for weighted tree automata over arbitrary, i.e., not necessarily commutative, semirings is derived. 1