Related papers: Uniformization and Skolem functions in the class o…

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…

The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese (1991). We prove the following problem is decidable: Input: (i) A monadic second…

Richard P. Stanley conjectured that finite trees can be distinguished by their chromatic symmetric functions. In this paper, we prove an analogous statement for posets: Finite rooted trees can be distinguished by their order quasisymmetric…

We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of…

This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…

Reduction trees are a way of encoding a substitution procedure dictated by the relations of an algebra. We use reduction trees in the subdivision algebra to construct canonical triangulations of flow polytopes which are shellable. We…

In this paper, estimates for Kolmogorov, Gelfand and linear widths of function classes on sets with a tree-like structure are obtained. As examples we consider weighted Sobolev classes on a John domain, as well as some function classes on a…

We consider Hilbert series associated to modules over various categories of trees. Using the technology of Sam and Snowden, we show that these Hilbert series must be algebraic. We then apply these technical theorems to prove facts about…

One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…

An extension of order theory is presented that serves as a formalism for the study of dendroidal sets analogously to way the formalism of order theory is used in the study of simplicial sets.

This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently…

The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…

A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…

Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…

In this paper, we study classes of structures and individual structures for which programs implementing functions defined everywhere are equivalent to finite tree-programs. The programs under consideration may have cycles and at most…

We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but…

A first-order theory has the Schroder-Bernstein property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove that if a countable theory T has the Schroder-Bernstein property then it is classifiable (it is…