Related papers: Slowly synchronizing automata and digraphs

We construct a time-optimal quasi-solution of the firing mob synchronisation problem over finite, connected, and undirected multigraphs whose maximum degrees are uniformly bounded by a constant. It is only a quasi-solution because its…

Under the assumption $\mathcal{P} \neq \mathcal{NP}$, we prove that two natural problems from the theory of synchronizing automata cannot be solved in polynomial time. The first problem is to decide whether a given reachable partial…

In this paper, we show that every D3-directing CNFA can be mapped uniquely to a DFA with the same synchronizing word length. This implies that \v{C}ern\'y's conjecture generalizes to CNFAs and that the general upper bound for the length of…

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…

Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…

This paper contains results related to synthesis and presentation of abstract automata by fragments of behaviour and investigates the structure of the classes of finite connected initial output-less automata specified by systems of defining…

The Fibonacci infinite word ${\bf f} = (f_i)_{i \geq 0} = 01001010\cdots$ is one of the most celebrated objects in combinatorics on words. There is a simple $5$-state automaton that, given $i$ in lsd-first Zeckendorf representation,…

We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a…

We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-machines in the language of automata theory and adapt a recent algorithm for…

The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…

We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of…

We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…

We establish the equivalence between a class of asynchronous distributed automata and a small fragment of least fixpoint logic, when restricted to finite directed graphs. More specifically, the logic we consider is (a variant of) the…

We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a…

When their reading heads are allowed to move completely asynchronously, finite-state automata with multiple tapes achieve a significant expressive power, but also lose useful closure properties---closure under intersection, in particular.…

Zielonka's theorem shows that each regular set of Mazurkiewicz traces can be implemented as a system of synchronized processes with a distributed control structure called asynchronous automaton. This paper gives a polynomial algorithm for…

The paper is concerned with defining the electrical signals and their models. The delays are discussed, the asynchronous automata - which are the models of the asynchronous circuits - and the examples of the clock generator and of the R-S…

We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…

Cerny's conjecture is a longstanding open problem in automata theory. We study two different concepts, which allow to approach it from a new angle. The first one is the triple rendezvous time, i.e., the length of the shortest word mapping…

We show that a well-known family of deterministic finite automata can be used to distinguish distinct binary strings of the same length from every start state. Further, we establish almost matching lower and upper bounds on the number of…