Max Dehn, Axel Thue, and the Undecidable

This is a short essay on the roles of Max Dehn and Axel Thue in the formulation of the word problem for (semi)groups, and the story of the proofs showing that the word problem is undecidable.Comment: Definition of undecidability and unsolvability improve

Multidimensional Generalized Automatic Sequences and Shape-symmetric Morphic Words

An infinite word is S-automatic if, for all n>=0, its (n + 1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for d>=2, we state that a multidimensional infinite word x : N^d \to \Sigma over a finite alphabet \Sigma is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word

Generic-case complexity, decision problems in group theory and random walks

We give a precise definition of ``generic-case complexity'' and show that for a very large class of finitely generated groups the classical decision problems of group theory - the word, conjugacy and membership problems - all have linear-time generic-case complexity. We prove such theorems by using the theory of random walks on regular graphs.Comment: Revised versio

Grouping Synonyms by Definitions

We present a method for grouping the synonyms of a lemma according to its dictionary senses. The senses are defined by a large machine readable dictionary for French, the TLFi (Tr\'esor de la langue fran\c{c}aise informatis\'e) and the synonyms are given by 5 synonym dictionaries (also for French). To evaluate the proposed method, we manually constructed a gold standard where for each (word, definition) pair and given the set of synonyms defined for that word by the 5 synonym dictionaries, 4 lexicographers specified the set of synonyms they judge adequate. While inter-annotator agreement ranges on that task from 67% to at best 88% depending on the annotator pair and on the synonym dictionary being considered, the automatic procedure we propose scores a precision of 67% and a recall of 71%. The proposed method is compared with related work namely, word sense disambiguation, synonym lexicon acquisition and WordNet construction