Related papers: Automatic Sequences and Zip-Specifications
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
In this paper we present a new family of discrete sequences having "random like" uniformly decaying auto-correlation properties. The new class of infinite length sequences are higher order chirps constructed using irrational numbers.…
The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…
A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analogue of Kleene's theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
To each one-dimensional subshift $X$, we may associate a winning shift $W(X)$ which arises from a combinatorial game played on the language of $X$. Previously it has been studied what properties of $X$ does $W(X)$ inherit. For example, $X$…
We study cyclic binary strings with bounds on the lengths of the intervals of consecutive ones and zeros. This is motivated by scheduling problems where such binary strings can be used to represent the state (on/off) of a machine. In this…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
Quantifying the degree of similarity between images is a key copyright issue for image-based machine learning. In legal doctrine however, determining the degree of similarity between works requires subjective analysis, and fact-finders…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
The Thue--Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors $w$ within this sequence, more precisely, the sequence of gaps between consecutive…
Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization…
We study the synchronous and asynchronous automatic structures on the fundamental group of a graph of groups in which each edge group is finite. Up to a natural equivalence relation, the set of biautomatic structures on such a graph product…
Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…
To a subshift over a finite alphabet, one can naturally associate an infinite family of finite graphs, called its Rauzy graphs. We show that for a subshift of subexponential complexity the Rauzy graphs converge to the line $\mathbf{Z}$ in…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
Linearizability is the de facto consistency condition for concurrent objects, widely used in theory and practice. Loosely speaking, linearizability classifies concurrent executions as correct if operations on shared objects appear to take…
Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. A core property is productivity: unfolding the equations produces the intended stream in the limit. In this…