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Bottomup and Topdown Tree Series Transformations
 J. Autom. Lang. Combin
, 2000
"... We generalize bottomup tree transducers and topdown tree transducers to the concept of bottomup tree series transducer and topdown tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from output trees to some s ..."
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Cited by 37 (6 self)
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We generalize bottomup tree transducers and topdown tree transducers to the concept of bottomup tree series transducer and topdown tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from output trees to some semiring. We associate two semantics with a tree series transducer: a mapping which transforms trees into tree series (for short: tree to tree series transformation or tts transformation), and a mapping which transforms tree series into tree series (for short: tree series transformation or tsts transformation). We show that the standard case of tree transducers is reobtained by choosing the boolean semiring under the tts semantics. Also, for each of the two types of tree series transducers and for both types of semantics, we prove a characterization which generalizes in a straightforward way the corresponding characterization result for the underlying tree transducer class. Mo...
Learning Functions Represented as Multiplicity Automata
, 2000
"... We study the learnability of multiplicity automata in Angluin’s exact learning model, and we investigate its applications. Our starting point is a known theorem from automata theory relating the ..."
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Cited by 27 (2 self)
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We study the learnability of multiplicity automata in Angluin’s exact learning model, and we investigate its applications. Our starting point is a known theorem from automata theory relating the
On the Applications of Multiplicity Automata in Learning
 In Proc. of the 37th Annu. IEEE Symp. on Foundations of Computer Science
, 1996
"... Recently the learnability of multiplicity automata [8, 24] attracted a lot of attention, mainly because of its implications on the learnability of several classes of DNF formulae [7]. In this paper we further study the learnability of multiplicity automata. Our starting point is a known theorem from ..."
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Cited by 20 (9 self)
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Recently the learnability of multiplicity automata [8, 24] attracted a lot of attention, mainly because of its implications on the learnability of several classes of DNF formulae [7]. In this paper we further study the learnability of multiplicity automata. Our starting point is a known theorem from automata theory relating the number of states in a minimal multiplicity automaton for a function f to the rank of a certain matrix F . With this theorem in hand we obtain the following results: ffl A new simple algorithm for learning multiplicity automata in the spirit of [24] with a better query complexity. As a result, we improve the complexity for all classes that use the algorithms of [8, 24] and also obtain the best query complexity for several classes known to be learnable by other methods such as decision trees [13] and polynomials over GF(2) [26]. ffl We prove the learnability of some new classes that were not known to be learnable before. Most notably, the class of polynomials ov...
A Kleene theorem for weighted tree automata
 Theory of Computing Systems
, 2002
"... In this paper we prove Kleene's result for tree series over a commutative and idempotent semiring A (which is not necessarily complete or continuous), i.e., the class of recognizable tree series over A and the class of rational tree series over A are equal. We show the result by direct automatatheo ..."
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Cited by 17 (8 self)
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In this paper we prove Kleene's result for tree series over a commutative and idempotent semiring A (which is not necessarily complete or continuous), i.e., the class of recognizable tree series over A and the class of rational tree series over A are equal. We show the result by direct automatatheoretic constructions and prove their correctness.
Algebraic Aspects of Bregular Series
, 1993
"... This paper concerns power series of an arithmetic nature that arise in the analysis of divideandconquer algorithms. Two key notions are studied: that of Bregular sequence and that of Mahlerian sequence with their associated power series. Firstly we emphasize the link between rational series over ..."
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Cited by 4 (1 self)
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This paper concerns power series of an arithmetic nature that arise in the analysis of divideandconquer algorithms. Two key notions are studied: that of Bregular sequence and that of Mahlerian sequence with their associated power series. Firstly we emphasize the link between rational series over the alphabet fx0 ; x1 ; : : : ; xB\Gamma1 g and Bregular series. Secondly we extend the theorem of Christol, Kamae, Mend`es France and Rauzy about automatic sequences and algebraic series to Bregular sequences and Mahlerian series. We develop here a constructive theory of Bregular and Mahlerian series. The examples show the ubiquitous character of Bregular series in the study of arithmetic functions related to number representation systems and divideandconquer algorithms.
Shrinking Language Models by Robust Approximation
 in Proc. IEEE Int'l. Conf. on Acoustics, Speech, and Signal Processing '98
, 1998
"... We study the problem of reducing the size of a language model while preserving recognition performance (accuracy and speed). A successful approach has been to represent language models by weighted finitestate automata (WFAs). Analogues of classical automata determinization and minimization algorith ..."
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Cited by 2 (2 self)
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We study the problem of reducing the size of a language model while preserving recognition performance (accuracy and speed). A successful approach has been to represent language models by weighted finitestate automata (WFAs). Analogues of classical automata determinization and minimization algorithms then provide a general method to produce smaller but equivalent WFAs. We extend this approach by introducing the notion of approximate determinization. We provide an algorithm that, when applied to language models for the North American Business task, achieves 2535% size reduction compared to previous techniques, with negligible effects on recognition time and accuracy. 1. INTRODUCTION An important goal of language model engineering is to produce small language models that guarantee fast and accurate automatic speech recognition (ASR). In practice we see tradeoffs: e.g., in size vs. accuracy and in accuracy vs. speed. There has been recent progress, however, on automatic methods for r...
Weighted logics for XML
, 2007
"... Abstract: We define a weighted monadic second order logic for XMLdocuments (weighted uMSOlogic), viewed as unranked trees. Such a logic allows us to pose quantitative queries to XMLdatabases. Also we define the concept of unranked weighted tree automata and prove that, for every commutative semir ..."
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Cited by 1 (0 self)
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Abstract: We define a weighted monadic second order logic for XMLdocuments (weighted uMSOlogic), viewed as unranked trees. Such a logic allows us to pose quantitative queries to XMLdatabases. Also we define the concept of unranked weighted tree automata and prove that, for every commutative semiring K, they have the same expressive power as (1) restricted weighted uMSOlogic, (2) almost existential weighted uMSOlogic whenever the additive monoid of K is locally finite, (3) (unrestricted) weighted uMSOlogic whenever K is locally finite. Moreover, if K is a computable field, then the equivalence of any two sentences of restricted weighted uMSOlogic is decidable and there is an effective procedure to construct the automaton from the sentence. 1
IIFS and codes (Extended Version)
, 1995
"... : In the beginning of the eighties, Hutchinson and Hata proposed a mechanism to describe fractal images which today is well known as iterated function systems (IFS). Subsequently, Marion, Barnsley, Mauldin, Williams, Bandt, Feiste, Culik and Dube suggested various ideas to generalize IFS. Some appr ..."
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: In the beginning of the eighties, Hutchinson and Hata proposed a mechanism to describe fractal images which today is well known as iterated function systems (IFS). Subsequently, Marion, Barnsley, Mauldin, Williams, Bandt, Feiste, Culik and Dube suggested various ideas to generalize IFS. Some approaches use formal language theory to describe parts of the address space in order to cut off pieces from the attractor of the IFS. Unfortunately, the formulae for calculating the Hausdorff dimension of suchdefined fractals are very clumsy. We shall present a setting wherein the Hausdorff dimension can be calculated quite easily using languagetheoretical arguments. Contents 1 Infinite IFS 3 2 Syntactic IIFS 8 3 Formal Language Issues 9 4 Problems and Outlook 19 Formal Outline: The first two sections of this paper serve to introduce some notions and important results from the theory of IIFS (function systems having an infinite number of mappings, a generalization of IFS). Detailed proofs for...