Characterisation of (Sub)sequential Rational Functions over a General Class Monoids

In this technical report we describe a general class of monoids for which (sub)sequential rational can be characterised in terms of a congruence relation in the flavour of Myhill-Nerode relation. The class of monoids that we consider can be described in terms of natural algebraic axioms, contains the free monoids, groups, the tropical monoid, and is closed under Cartesian.

Corpus analysis without prior linguistic knowledge - unsupervised mining of phrases and subphrase structure

When looking at the structure of natural language, "phrases" and "words" are central notions. We consider the problem of identifying such "meaningful subparts" of language of any length and underlying composition principles in a completely corpus-based and language-independent way without using any kind of prior linguistic knowledge. Unsupervised methods for identifying "phrases", mining subphrase structure and finding words in a fully automated way are described. This can be considered as a step towards automatically computing a "general dictionary and grammar of the corpus". We hope that in the long run variants of our approach turn out to be useful for other kind of sequence data as well, such as, e.g., speech, genom sequences, or music annotation. Even if we are not primarily interested in immediate applications, results obtained for a variety of languages show that our methods are interesting for many practical tasks in text mining, terminology extraction and lexicography, search engine technology, and related fields.

Good parts first - a new algorithm for approximate search in lexica and string databases

We present a new efficient method for approximate search in electronic lexica. Given an input string (the pattern) and a similarity threshold, the algorithm retrieves all entries of the lexicon that are sufficiently similar to the pattern. Search is organized in subsearches that always start with an exact partial match where a substring of the input pattern is aligned with a substring of a lexicon word. Afterwards this partial match is extended stepwise to larger substrings. For aligning further parts of the pattern with corresponding parts of lexicon entries, more errors are tolerated at each subsequent step. For supporting this alignment order, which may start at any part of the pattern, the lexicon is represented as a structure that enables immediate access to any substring of a lexicon word and permits the extension of such substrings in both directions. Experimental evaluations of the approximate search procedure are given that show significant efficiency improvements compared to existing techniques. Since the technique can be used for large error bounds it offers interesting possibilities for approximate search in special collections of "long" strings, such as phrases, sentences, or book ti