The words of a context-free language, ordered by the lexicographic ordering, form a context-free linear ordering. It is well-known that the linear orderings associated with deterministic context-free languages have a decidable monadic second-order theory. In stark contrast, we give an example of a context-free language whose lexicographic ordering has an undecidable first-order theory.

abstract. let (r,p) be a noetherian unique factorization do-main (ufd) and m be a finitely generated r-module. let i(m)be the first nonzero fitting ideal of m and the order of m, denotedord_r(m), be the largest integer n such that i(m) ⊆ p^n. in thispaper, we show that if m is a module of order one, then either mis isomorphic with direct sum of a free module and a cyclic moduleor m is isomorphi...

It is well known that some of the most basic properties of words, like the commutativity (xy = yx) and the conjugacy (xz = zy), can be expressed as solutions of word equations. An important problem is to decide whether or not a given equation on words has a solution. For instance, the equation xmyn = zp has only periodic solutions in a free monoid, that is, if xmyn = zp holds with integers m,n,...

We study the analyticity properties of the free energy fγ(m) of the Kac model at points of first order phase transition, in the van der Waals limit γ ↘ 0. We show that there exists an inverse temperature β0 and γ0 > 0 such that for all β ≥ β0 and for all γ ∈ (0, γ0), fγ(m) has no analytic continuation along the path m ↘ m∗ (m∗ denotes spontaneous magnetization). The proof consists in studying h...

Let A be a finite, totally ordered alphabet, and let P be the lexicographic ordering on A*. Let X be a subset of A*. The language of minimal words of X is the subset of X composed of the lexicographically minimal word of X for each length: Min(X)=[x # X | \w # X, |w|=|x| O xPw]. The aim of this paper is to prove that if L is a context-free language, then the language Min(L) context-free. ] 1997

We prove that a finitely generated group is context-free whenever its Cayleygraph has a decidable monadic second-order theory. Hence, by the seminal work of Muller and Schupp, our result gives a logical characterization of context-free groups and also proves a conjecture of Schupp. To derive this result, we investigate general graphs and show that a graph of bounded degree with a high degree of...