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A homomorphism of an automaton ${\bf A}$ without outputs onto a subautomaton ${\bf B}$ of ${\bf A}$ is called a retract homomorphism if it leaves the elements of $B$ fixed. An automaton ${\bf A}$ is called a retractable automaton if, for…
A complete deterministic finite automaton in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize completely…
The notion of an automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ is used to define and study automorphism groups of the tree $X^*$ of finite words over $X$. The concept of bi-reversibility for Mealy-type automata is extended to…
A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration.…
For any nontrivial abelian group $\mathbb{X}$ we construct a reversible (bireversible in case the order of $\mathbb{X}$ is odd) automaton such that its set of states and alphabet are identified with $\mathbb{X}$, transition and output…
We introduce the category of dependency automata. A dependency automaton consists of two nondeterministic finite automata, with a relation between their states satisfying conditions. This category is equivalent to deterministic finite…
A typewriter automaton is a special variant of a two-dimensional automaton that receives two-dimensional words as input and is only capable of moving its input head through its input word in three directions: downward, leftward, and…
A dynamic logic ${\mathbf B}$ can be assigned to every automaton ${\mathcal A}$ without regard if ${\mathcal A}$ is deterministic or nondeterministic. This logic enables us to formulate observations on ${\mathcal A}$ in the form of composed…
We consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
A random boolean cellular automaton is a network of boolean gates where the inputs, the boolean function, and the initial state of each gate are chosen randomly. In this article, each gate has two inputs. Let $a$ (respectively $c$) be the…
Semi-automata are abstractions of electronic devices that are deterministic finite-state machines having inputs but no outputs. Generalized semiautomata are obtained from stochastic semiautomata by dropping the restrictions imposed by…
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…
Higher-dimensional automata constitute a very expressive model for concurrent systems. In this paper, we discuss "topological abstraction" of higher-dimensional automata, i.e., the replacement of HDAs by smaller ones that can be considered…
The main results of this paper is to give a complete characterization of the automaticity of one-relator semigroups with length less than or equal to three. Let $S=sgp\langle A|u=v\rangle$ be a semigroup generated by a set…
Subzero automata is a class of tree automata whose acceptance condition can express probabilistic constraints. Our main result is that the problem of determining if a subzero automaton accepts some regular tree is decidable.
A deterministic finite automaton 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 is called completely reachable. We characterize such automata in terms of graphs…
Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is…
Fungal automata are a variation of the two-dimensional sandpile automaton of Bak, Tang, and Wiesenfeld (Phys. Rev. Lett. 1987). In each step toppling cells emit grains only to some of their neighbors chosen according to a specific update…
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…