On certain recurrent and automatic sequences in finite fields

In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first author in connection with algebraic continued fractions. By including it in a large family of recurrent sequences in an arbitrary finite field, we prove its automaticity. Then we give a criterion on automatic sequences, generalizing a previous result and this allows us to present new families of automatic sequences in an arbitrary finite field.Comment: 10 page

Hyperquadratic continued fractions over a finite field of odd characteristic with partial quotients of degree 1

In 1986, some examples of algebraic, and nonquadratic, power series over a finite prime field, having a continued fraction expansion with partial quotients all of degree one, were discovered by W. Mills and D. Robbins. In this note we show how these few examples are included in a very large family of continued fractions for certain algebraic power series over an arbitrary finite field of odd characteristic

Rational approximations to algebraic Laurent series with coefficients in a finite field

In this paper we give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improve this general bound in many cases. As an illustration, we give few examples of algebraic Laurent series for which we are able to compute the exact value of the irrationality exponent

Research on the utilization of pattern recognition techniques to identify and classify objects in video data Final report

Spaceborne pattern recognition system for identifying and classifying objects in video dat

HYPERQUADRATIC CONTINUED FRACTIONS AND AUTOMATIC SEQUENCES

The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. This connection is illustrated by three families of examples and a counterexample