Related papers: Morphisms on infinite alphabets, countable states …
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
We study the automorphisms of binary stabilizer codes and states. We prove that they almost always form a solvable group, and thereby shed new light on the fact that there is no universal set of transversal gates. We also determine the…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
Automatic structures are infinite structures that are finitely represented by synchronized finite-state automata. This paper concerns specifically automatic structures over finite words and trees (ranked/unranked). We investigate the…
In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first…
If an automorphism f of a structure M is such that fix(f^k) = fix(f) for all positive k, then M|fix(f) is a substructure of M. The possible isomorphism types of such M|fix(f) are characterized when M is countable and arithmetically…
In this article we present a unified way to smooth certain multiple structures called ropes on smooth varieties. We prove that most ropes of arbitrary multiplicity, supported on smooth curves can be smoothed. By a rope being smoothable we…
We give an unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFAs) with n states over an alphabet of k symbols. We show how to generate all these strings for each n and k, and how its…
In this article we generalize a theorem of Benson for generalized quadrangles to strongly regular graphs and directed strongly regular graphs. The main result provides numerical restrictions on the number of fixed vertices and the number of…
We exhibit invariants of smooth projective algebraic varieties with integer values, whose nonvanishing modulo p prevents the existence of an action without fixed points of certain finite p-groups. The case of base fields of characteristic p…
We prove that if $y=\sum_{n=0}^\infty{\bf a}(n)x^n\in\mathbb{F}_q[[x]]$ is an algebraic power series of degree $d$, height $h$, and genus $g$, then the sequence ${\bf a}$ is generated by an automaton with at most $q^{h+d+g-1}$ states, up to…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
The article defines and studies the genus of finite state deterministic automata (FSA) and regular languages. Indeed, a FSA can be seen as a graph for which the notion of genus arises. At the same time, a FSA has a semantics via its…
Automata operating on general graphs have been introduced by virtue of graphoids. In this paper we construct a graph automaton that recognizes $k$-colorable graphs.
We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…
In this paper we consider the problem of proving properties of infinite behaviour of formalisms suitable to describe (infinite state) systems with recursion and parallelism. As a formal setting, we consider the framework of Process…
We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are periodic away from a finite set. Using methods from ergodic theory, we are able to partially…
Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs…
We make certain bounds in Krebs' proof of Cobham's theorem explicit and obtain corresponding upper bounds on the length of a common prefix of an aperiodic $a$-automatic sequence and an aperiodic $b$-automatic sequence, where $a$ and $b$ are…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…