We generalize bottom-up tree transducers and top-down tree transducers to the concept of bottom-up tree series transducer and top-down 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 t-ts transformation), and a mapping which transforms tree series into tree series (for short: tree series transformation or ts-ts transformation). We show that the standard case of tree transducers is reobtained by choosing the boolean semiring under the t-ts 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...

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...

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

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 automata-theoretic constructions and prove their correctness.

This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-conquer algorithms. Two key notions are studied: that of B-regular 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 B-regular series. Secondly we extend the theorem of Christol, Kamae, Mend`es France and Rauzy about automatic sequences and algebraic series to B-regular sequences and Mahlerian series. We develop here a constructive theory of B-regular and Mahlerian series. The examples show the ubiquitous character of B-regular series in the study of arithmetic functions related to number representation systems and divide-and-conquer algorithms.

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 finite-state 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 25--35% 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...

: 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 such-defined 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...

Abstract: We define a weighted monadic second order logic for XML-documents (weighted uMSO-logic), viewed as unranked trees. Such a logic allows us to pose quantitative queries to XML-databases. 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 uMSO-logic, (2) almost existential weighted uMSO-logic whenever the additive monoid of K is locally finite, (3) (unrestricted) weighted uMSO-logic whenever K is locally finite. Moreover, if K is a computable field, then the equivalence of any two sentences of restricted weighted uMSO-logic is decidable and there is an effective procedure to construct the automaton from the sentence. 1

Abstract: We investigate weighted finite automata over strings and strong bimonoids. Such algebraic structures satisfy the same laws as semirings except that no distributivity laws need to hold. We define two different behaviors and prove precise characterizations for them if the underlying strong bimonoid satisfies local finiteness conditions. Moreover, we show that in this case the given weighted automata can be determinized. 1