A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e. the infinite sequences of cell states. The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evol...

The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton semigroup. We also show that the class of automaton semigroups is closed under the combined operation of ‘free product followed by adjoining an identity’. W...

We present an algorithm to generate positive braids of a given length as words in Artin generators with a uniform probability. The complexity of this algorithm is polynomial in the number of strands and in the length of the generated braids. As a byproduct, we describe a finite state automaton accepting the language of lexicographically minimal representatives of positive braids that has the mi...

In this paper, we present a method for computing the set of reachable states for networks consisting of the parallel composition of a finite number of the same hybrid automaton template with rectangular dynamics. The method utilizes a symmetric representation of the set of reachable states (modulo the automata indices) that we call anonymized states, which makes it scalable. Rather than explici...

Thě Cern´y's conjecture states that for every synchronizing automaton with n states there exists a reset word of length not exceeding (n−1) 2. We prove this conjecture for a class of automata preserving certain properties of intervals of a directed graph. Our result unifies and generalizes some earlier results obtained by other authors. In this paper we consider finite (deterministic complete) ...

In [3], Ilie and Yu describe a construction of a right-invariant equivalence relation on the states of a non-deterministic finite-state automaton. We give a more efficient algorithm for constructing the same equivalence, together with results from a computer implementation.

In languages over a unary alphabet, i.e., an alphabet with only one letter, words can be identified with their lengths. It is well known that each regular language over a unary alphabet can be represented as the union of a finite number of arithmetic progressions. Given a nondeterministic finite automaton (NFA) working over a unary alphabet (a unary NFA), the arithmetic progressions representin...