Showing papers on "Continuous automaton published in 1967"

Adaptation of stochastic automata in nonstationary environments

Abstract: This paper considers the effect of environmental nonstationarities on the performance of a stochastic automaton when it is used in the synthesis of an adaptive controller. The stochastic automaton considered has a variable structure in that its state probabilities are continuously altered according to a reinforcement scheme in response to penalties received from the environment. The automaton adapts by reducing the average penalty. Periodic perturbations of penalty strengths are used as "test signals" to derive analytic expressions describing the "tracking" behavior of the automaton operating under a linear reinforcement scheme. The pertinent parameters governing the adaptive behavior are discussed in detail. Digital simulation studies are presented for 2-state and 10-state cases. The results agree with the theoretical analysis.

Some results on the set of congruence relations in a finite, strongly connected automaton

Abstract: The congruence relations of an automaton are of interest for various reasons For example they are relevant for minimization procedures and they are suitable for decomposing the automaton in a specific way which is of technical importance [Hartmanis et al] In this paper we have investigated the interconnection between the automorphism groupG (A) and the latticeR (A) of congruence relations of an automaton This interconnection is primarily based on a Galois connection between the subgroup lattice ofG (A) and the latticeG (A), which characterizes a subset ofR (A) in terms of groups Assuming that group theory is the trivial part of the theory of semigroups, the attention is directed to the remainder ofR (A) which is not characterized byG (A) in the way mentioned above This remainder, however, has not been inspected for the general case, which seems to be a hopeless task, but for the class of so called right regular automata In the last section some theoretical background for a systematic procedure in obtaining all congruence relations of an automaton as well as its endomorphism semigroup has been developed