The first-order isomorphism problem is to decide whether two non-recursive types using product- and function-type constructors are isomorphic under the axioms of commutative and associative products, and currying and distributivity of functions over products. We show that this problem can be solved in $O(n \log^2 n)$ time and $O(n)$ space, where $n$ is the input size. This result improves upon the $O(n^2 \log n)$ time and $O(n^2)$ space bounds of the best previous algorithm. We also describe an $O(n)$ time algorithm for the linear isomorphism problem, which does not include the distributive axiom, thereby improving upon the $O(n \log n)$ time of the best previous algorithm for this problem.

It is interesting to note that the very first papers related to isomorphism of types were written before the notion itself appeared. Their subjects were the study of equality of terms defined on numbers, the isomorphism of objects in certain categories and the invertibility of $\lambda$-terms, but not the isomorphism of types ‘as such’. One may cite the so-called ‘Tarsky High School Algebra Problem’: whether all identities between terms built from $+, x, \uparrow$, variables and constants are derivable from basic ‘high school equalities’, like $(xy)^z=x^zy^z$. The earliest publications related to this problem date from the 1940s, cf. Birkhoff (1940) – an extensive bibliography may be found in Burris and Yeats (2002).

We consider shifted equality sets of the form EG(a,g1,g2) = {ω | g1(ω) = ag2(ω)}, where g 1 and g 2 are nonerasingmorphisms and a is a letter. We are interested in the familyconsisting of the languages h(EG(J)), where h is a coding and(EG(J)) is a shifted equality set. We prove several closureproperties for this family. Moreover, we show that everyrecursively enumerable language L ⊆ A* is a projectionof a shifted equality set, that is, L = πA(EG(a,g1,g2)) for some (nonerasing) morphisms g 1 and g 2 and aletter a, where πA deletes the letters not in A. Thenwe deduce that recursively enumerable star languages coincide withthe projections of equality sets.

We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).

We give necessary and sufficient conditions for a language to be the language of finite words that occur infinitely many times in an infinite word.

The paper presents an elementary approach for the calculation of the entropyof a class of languages. This approach is based on the consideration ofroots of a real polynomial and is also suitable for calculating theBernoulli measure. The class of languages we consider here is ageneralisation of the Łukasiewicz language.

Dans cet article, nous exploitons la réductibilité d'unpolynômed'une variable pour calculer efficacement l'idéal des relationsalgébriques entre ses racines.

We study deterministic one-way communication complexity of functions with Hankel communication matrices. Some structural properties of such matrices are establishedand applied to the one-way two-party communication complexity of symmetric Boolean functions.It is shown that the number of required communication bits does not depend on the communication direction, provided thatneither direction needs maximum complexity. Moreover, in order to obtain an optimal protocol, it is in any case sufficient to consider only the communication directionfrom the party with the shorter input to the other party. These facts do not hold for arbitrary Boolean functions in general. Next, gaps between one-way and two-way communication complexity for symmetric Boolean functions are discussed.Finally, we give some generalizations to the case of multiple parties.

In previous work (Gough and Way 2004), we showed that our Example-Based Machine Translation (EBMT) system improved with respect to both coverage and quality when seeded with increasing amounts of training data, so that it significantly outperformed the on-line MT system Logomedia according to a wide variety of automatic evaluation metrics. While it is perhaps unsurprising that system performance is correlated with the amount of training data, we address in this paper the question of whether a large-scale, robust EBMT system such as ours can outperform a Statistical Machine Translation (SMT) system. We obtained a large English-French translation memory from Sun Microsystems from which we randomly extracted a near 4K test set. The remaining data was split into three training sets, of roughly 50K, 100K and 200K sentence-pairs in order to measure the effect of increasing the size of the training data on the performance of the two systems. Our main observation is that contrary to perceived wisdom in the field, there appears to be little substance to the claim that SMT systems are guaranteed to outperform EBMT systems when confronted with ‘enough’ training data. Our tests on a 4.8 million word bitext indicate that while SMT appears to outperform our system for French-English on a number of metrics, for English-French, on all but one automatic evaluation metric, the performance of our EBMT system is superior to the baseline SMT model.

This paper presents a very simple and effective approach to using parallel corpora for automatic bilingual lexicon acquisition. The approach, which uses the Random Indexing vector space methodology, is based on finding correlations between terms based on their distributional characteristics. The approach requires a minimum of preprocessing and linguistic knowledge, and is efficient, fast and scalable. In this paper, we explain how our approach differs from traditional cooccurrence-based word alignment algorithms, and we demonstrate how to extract bilingual lexica using the Random Indexing approach applied to aligned parallel data. The acquired lexica are evaluated by comparing them to manually compiled gold standards, and we report overlap of around 60%. We also discuss methodological problems with evaluating lexical resources of this kind.

Parallel texts have become a vital element for natural language processing. We present a panorama of current research activities related to parallel texts, and offer some thoughts about the future of this rich field of investigation.

Statistical, linguistic, and heuristic clues can be used for the alignment of words and multi-word units in parallel texts. This article describes the clue alignment approach and the optimization of its parameters using a genetic algorithm. Word alignment clues can come from various sources such as statistical alignment models, co-occurrence tests, string similarity scores and static dictionaries. A genetic algorithm implementing an evolutionary procedure can be used to optimize the parameters necessary for combining available clues. Experiments on English/Swedish bitext show a significant improvement of about 6% in F-scores compared to the baseline produced by statistical word alignment.Most of the work described in this paper was carried out at the Department of Linguistics and Philology at Uppsala University. I would like to acknowledge technical and scientific support by people at the department in Uppsala.

Broad coverage, high quality parsers are available for only a handful of languages. A prerequisite for developing broad coverage parsers for more languages is the annotation of text with the desired linguistic representations (also known as “treebanking”). However, syntactic annotation is a labor intensive and time-consuming process, and it is difficult to find linguistically annotated text in sufficient quantities. In this article, we explore using parallel text to help solving the problem of creating syntactic annotation in more languages. The central idea is to annotate the English side of a parallel corpus, project the analysis to the second language, and then train a stochastic analyzer on the resulting noisy annotations. We discuss our background assumptions, describe an initial study on the “projectability” of syntactic relations, and then present two experiments in which stochastic parsers are developed with minimal human intervention via projection from English.

In this article we illustrate and evaluate an approach to create high quality linguistically annotated resources based on the exploitation of aligned parallel corpora. This approach is based on the assumption that if a text in one language has been annotated and its translation has not, annotations can be transferred from the source text to the target using word alignment as a bridge. The transfer approach has been tested and extensively applied for the creation of the MultiSemCor corpus, an English/Italian parallel corpus created on the basis of the English SemCor corpus. In MultiSemCor the texts are aligned at the word level and word sense annotated with a shared inventory of senses. A number of experiments have been carried out to evaluate the different steps involved in the methodology and the results suggest that the transfer approach is one promising solution to the resource bottleneck. First, it leads to the creation of a parallel corpus, which represents a crucial resource per se. Second, it allows for the exploitation of existing (mostly English) annotated resources to bootstrap the creation of annotated corpora in new (resource-poor) languages with greatly reduced human effort.

Standard parameter estimation schemes for statistical translation models can struggle to find reasonable settings on some parallel corpora. We show how auxiliary information can be used to constrain the procedure directly by restricting the set of alignments explored during parameter estimation. This enables the integration of bilingual and monolingual knowledge sources while retaining the flexibility of the underlying models. We demonstrate the effectiveness of this approach for incorporating linguistic and domain-specific constraints on various parallel corpora, and consider the importance of using the context of the parallel text to guide the application of such constraints.