Related papers: Automata in toposes, and general Myhill-Nerode the…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
A definition of a probabilistic automaton is formulated in which its prime decomposition follows as a direct consequence of Krohn-Rhodes theorem. We first characterize the local structure of probabilistic automata. The prime decomposition…
We establish a set-oriented algorithm for the numerical approximation of the rotation set of homeomorphisms of the two-torus homotopic to the identity. A theoretical background is given by the concept of {\epsilon}-rotation sets. These are…
In this paper, we give a Nivat-like characterization for weighted alternating automata over commutative semirings (WAFA). To this purpose we prove that weighted alternating can be characterized as the concatenation of weighted finite tree…
We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata)…
For each $n, d \in \mathbb{N}$ and $0 < \alpha < 1$, we define a random subset of $\mathcal{A}^{\{1, 2, \dots, n\}^d}$ by independently including each element with probability $\alpha$ and excluding it with probability $1-\alpha$, and…
We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic. Using methods from ergodic theory, we are able to partially resolve this…
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…
This paper discusses iterated monodromy groups for transcendental functions. We show that for every post-singularly finite entire transcendental function, the iterated monodromy action can be described by bounded activity automata of a…
Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their…
We present a general coalgebraic setting in which we define finite and infinite behaviour with B\"uchi acceptance condition for systems whose type is a monad. The first part of the paper is devoted to presenting a construction of a monad…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…
We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not…
In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or…
In this technical report we describe a general class of monoids for which (sub)sequential rational can be characterised in terms of a congruence relation in the flavour of Myhill-Nerode relation. The class of monoids that we consider can be…
We give another proof of a theorem of Fife - understood broadly as providing a finite automaton that gives a complete description of all infinite binary overlap-free words. Our proof is significantly simpler than those in the literature. As…
In this paper we regard languages and their acceptors -- such as deterministic or weighted automata, transducers, or monoids -- as functors from input categories that specify the type of the languages and of the machines to categories that…
We devise an algorithm which, given a bounded automaton A, decides whether the group generated by A is finite. The solution comes from a description of the infinite sequences having an infinite A-orbit using a deterministic finite-state…
Motivated by the \v{C}ern\'y conjecture for automata, we introduce the concept of monoidal automata, which allows the formulation of the \v{C}ern\'y conjecture for monoids. We show upper bounds on the reset threshold of monoids with certain…