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.

On the transparency of automata as discrete-event control specifications

Abstract: The problem of maximizing the transparency of specification automata for discrete event systems (DES's) is investigated. In a transparent specification automaton, events that are irrelevant to the specification but can occur in the system are ‘hidden’ in self-loops. Different automata of the same specification on a DES can be associated with different sets of such irrelevant events; and any such automaton is said to be the most transparent if it has an irrelevant event set of maximal cardinality. The transparency maximization problem is theoretically formulated and a provably correct solution algorithm is obtained. The most transparent specification automaton essentially shows the precedence ordering among events from a minimal cardinality set that is relevant to the intended requirement, and should help towards resolving the long-standing problem in specification, namely: how do we know that a specification in automata does indeed capture the intended control requirement?

Bounded-transient automata

Abstract: A bounded-transient finite automaton is an automaton for which a single change of an input will not affect the output "far away." This paper investigates the class of events which bounded-transient automata can compute and shows that this class of events is a generalization of the class of definite events. A method of determining whether or not a finite automaton is bounded-transient is described, and the connection between the results of this paper and Kilmer's results is indicated.

Automata Recognizing No Words: A Statistical Approach

Abstract: How likely is that a randomly given (non-) deterministic finite automaton recognizes no word? A quick reflection seems to indicate that not too many finite automata accept no word; but, can this intuition be confirmed? In this paper we offer a statistical approach which allows us to conclude that for automata, with a large enough number of states, the probability that a given (non-) deterministic finite automaton recognizes no word is close to zero. More precisely, we will show, with a high degree of accuracy (i.e., with precision higher than 99% and level of confidence 0.9973), that for both deterministic and non-deterministic finite automata: a) the probability that an automaton recognizes no word tends to zero when the number of states and the number of letters in the alphabet tend to infinity, b) if the number of states is fixed and rather small, then even if the number of letters of the alphabet of the automaton tends to infinity, the probability is strictly positive. The result a) is obtained via a statistical analysis; for b) we use a combinatorial and statistical analysis. The present analysis shows that for all practical purposes the fraction of automata recognizing no words tends to zero when the number of states and the number of letters in the alphabet grow indefinitely. From a theoretical point of view, the result can motivate the search for "certitude" that is, a proof of the fact established here in probabilistic terms. In the last section we critically discuss the result and the method used in this paper.

5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

Abstract: We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA.