Related papers: Auto-similarity in rational base number systems

We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations), in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple…

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces…

This paper studies the minimal length representation of the natural numbers. Let O be a fixed set of integer-valued functions (primarily hyperoperations). For each n, what is the shortest way of expressing n as a combinations of functions…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

It is shown that a group defined by forbidding all patterns of size s+1 that do not appear in a given self-similar group of tree automorphisms is the topological closure of a self-similar, countable, regular branch group, branching over its…

A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…

A graph $G$ is defined encapsulating the number theoretic notion of the Fundamental Theorem of Arithmetic. We then provide a graph theoretic approach to the fundamental results on the coprimality of two natural numbers, through the use of…

An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any…

We show that every trace monoid is isomorphic to a sub-monoid of a monoid of word vectors. It provides a concrete representation of the elements of a trace monoid as processes associated with a resource sharing mechanism. We illustrate this…

We present graph-based translation models which translate source graphs into target strings. Source graphs are constructed from dependency trees with extra links so that non-syntactic phrases are connected. Inspired by phrase-based models,…

We propose to study transformations on graphs, and more generally structures, by looking at how the cut-rank (as introduced by Oum) of subsets is affected when going from the input structure to the output structure. We consider…

This paper grew out of three tutorial lectures on automatic structures given by the first author at the Logic Colloquium 2007. We discuss variants of automatic structures related to several models of computation: word automata, tree…

Motivated by multiplication algorithms based on redundant number representations, we study representations of an integer $n$ as a sum $n=\sum_k \epsilon_k U_k$, where the digits $\epsilon_k$ are taken from a finite alphabet $\Sigma$ and…

For a text given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering…

We investigate the following problem: given a sample of classified strings, find a first-order sentence of minimal quantifier rank that is consistent with the sample. We represent strings as successor string structures, that is, finite…

In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…

In computer science, especially when dealing with quantum computing or other non-standard models of computation, basic notions in probability theory like "a predicate" vary wildly. There seems to be one constant: the only useful example of…

Consider a connected graph $G=(E,V)$ with $N=|V|$ vertices. The main purpose of this paper is to explore the question of uniform sampling of a subtree of $G$ with $n$ nodes, for some $n\leq N$ (the spanning tree case correspond to $n=N$,…

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set…

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…