In this paper we describe several theorems that give lower bounds on the second eigenvalue of any quotient of a given size of a fixed graph, G. These theorems generalize Alon-Boppana type theorems, where G is a regular (infinite) tree. When G is a hypercube, our theorems give minimum distance upper bounds on linear binary codes of a given size and information rate. Our bounds at best equal the ...

We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weak converges to the symmetric mixture of the Ising model with + boundary conditions and the − boundary conditions on the k-regular tree with inverse temperature β. In the case where the ...

We present an approach to obtain language models from a tree corpus using probabilistic regular tree grammars (prtg). Starting with a prtg only generating trees from the corpus, the prtg is generalized step by step by merging nonterminals. We focus on bottom-up deterministic prtg to simplify the calculations.

This paper presents our compilation strategy to produce efficient code for pattern matching in the CDuce compiler, taking into account static information provided by the type system.

This thesis applies the theory of Anti-Unification modulo Equational Theory (E-Anti-Unification, E-Generalization) to proportional analogies in the string domain. Human solving of proportional analogies of the form A : B :: C : D (read: A is to B like C to D, where A,B and C are given) is modelled by an approach originally developed by Heinz [1996], refined in Burghardt [2005]. The goal is to g...

We explore the structure of the p-adic automorphism group Γ of the infinite rooted regular tree. We determine the asymptotic order of a typical element, answering an old question of Turán. We initiate the study of a general dimension theory of groups acting on rooted trees. We describe the relationship between dimension and other properties of groups such as solvability, existence of dense free...

Let Tn be a (d − 1)-ary tree of height n. A bilateral regular tree is the multigraph T d n,n that is defined by : (i) juxtaposing two Tn’s, (ii) drawing a new edge between two roots and (iii) drawing d− 1 edges between each leaf and a new vertex, called the sink. In this paper the sandpile group of T d n,n is determined.

Programming language syntax is often described by means of a context-free grammar, which is restricted by constraints programmed into the action code associated with productions. Without such code, the grammar would explode in size if it were to describe the same language. We present the tool YakYak, which extends Yacc with rst-order logic for specifying constraints that are regular tree langua...

Macro tree transducers (mtt) are an important model that both covers many useful XML transformations and allows decidable exact typechecking. This paper reports our first step toward an implementation of mtt typechecker that has a practical efficiency. Our approach is to represent an input type obtained from a backward inference as an alternating tree automaton, in a style similar to Tozawa’s X...

The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in DynPROP exactly are the regular languages, even when allowing arbitrary preco...