Jean-Michel Autebert

Context-free languages and pushdown automata

This chapter is devoted to context-free languages. Context-free languages and grammars were designed initially to formalize grammatical properties of natural languages [9]. They subsequently appeared to be well adapted to the formal description of the syntax of programming languages. This led to a considerable development of the theory.

Quelques problèmes ouverts en théorie des langages algébriques

— We present hère some open questions about the context-free languages.

Groups and NTS languages

Abstract The context-free groups are known to be exactly the finitely generated virtually free groups [19, 11]. We give here a new combinatorial property which characterizes these groups: they are “locally primary.” A corollary of this property is that the cylinder generated by the group languages is included in the family of NTS languages. In particular, every context-free group language is NTS.

Prefixes of infinite words and ambiguous context-free languages

Abstract Two ‘gap’ theorems are shown for languages formed with words that fail to be prefixes of an infinite word: such languages can never be described by unambiguous context-free grammars.

VERY SMALL FAMILIES OF ALGEBRAIC NONRATIONAL LANGUAGES

Publisher Summary One of the purposes of formal language theory is to propose some notions that enable deriving from local properties of words and global properties of languages. This point of view justifies all the studies on regularity in words of rational or algebraic languages. There are more conjectures than results in this area, and there is no known characterization of algebraic languages that are rational in terms of local properties on their words. The problem is closely related to the study of algebraic languages that are rational and to the questions about very small rational cones. The languages that are nearly rational deal with a characterization of rationality of algebraic languages. This chapter discusses some results obtained on the problem of minimal cones and necessary conditions are given by the iteration theorems for rational languages; among these, the most powerful one is the Ogden-like version of the star theorem. Moreover, the study of algebraic languages leads to defining different kinds of iterative pairs.

On Generalized Delannoy Paths

A Delannoy path is a minimal path with diagonal steps in

A note on 1-locally linear languages

{\mathbb Z}^2

The equivalence of pre-NTS grammars is decidable

between two arbitrary points. We extend this notion to the n dimensions space

GENERATORS OF CONES AND CYLINDERS

{\mathbb Z}^n

Indécidabilité de la condition IRS

and identify such paths with words on a special kind of alphabet: an S-alphabet. We show that the set of all the words corresponding to Delannoy paths going from one point to another is exactly one class in the congruence generated by a Thue system that we exhibit. This Thue system induces a partial order on this set that is isomorphic to the set of ordered partitions of a fixed multiset where the blocks are sets with a natural order relation. Our main result is that this poset is a lattice.