ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

Optimal simulations of weak restarting automata

Abstract: The simulation of weak restarting automata, i.e., classical restarting automata accepting exactly the regular languages, by finite automata is studied. Some of the trade-offs in the number of states when changing the representation are known. Here we continue the investigation in order to draw an almost complete picture of the descriptional power gained in the additional structural resources of weak restarting automata. In particular, for det-RR(1)-simulations of nondeterministic finite automata we obtain the same tight bounds as for simulations of R(1)-automata, though in some cases the latter class is much more efficient than the former. Moreover, the DFA-simulation of det-RR(1)-automata is considered. The shown bounds are of factorial order and are tight. The constructions are via alternating finite automata to DFAs. So, in addition, an upper bound for the AFA-simulation is obtained.

Experiments with automata when the upper bound of the number of their states is unknown

Abstract: The properties of a class of initial finite automata are investigated; the class is possibly infinite, and each input-output signal of a fixed set of automata from this class is produced by no more than one state. The exact finiteness conditions of this class and its important subclasses and exact existence conditions of check experiments related to these classes are found. The existence conditions of experiments on recognition of such automata are also described.

Representing Small Ordinals by Finite Automata

Abstract: It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than omega^omega. We design a polynomial time algorithm that constructs, for each well-ordered regular language L with respect to the lexicographic ordering, given by a deterministic finite automaton, the Cantor Normal Form of its order type. It follows that there is a polynomial time algorithm to decide whether two deterministic finite automata accepting well-ordered regular languages accept isomorphic languages. We also give estimates on the size of the smallest automaton representing an ordinal less than omega^omega, together with an algorithm that translates each such ordinal to an automaton.

Dynamic Behaviour of Chaotic Cellular Automata - A Comparative Entropy Analysis of Regular Lattices and Small-World Structures

Abstract: This work investigates elementary cellular automata comparing their dynamic evolution on two topologies: the usual regular lattice and a small-world network constructed as a directed graph. The number of iterations for any initial perturbation to propagate over all cells of the automaton corresponds to how quickly an initial configuration reaches a high entropy state, and the temporal rate of propagation of the perturbation can be evaluated from a chaotic set of elementary cellular automata rules using an entropy measure. Results indicate that the average entropy can be nearly tripled in the small-world network topology, suggesting much faster applications (e.g. in Cryptography) from alterations in the topological arrangement of usual cellular automata regular lattices.