本课题的研究对象是正特征域上由自动机序列定义的连分式的代数性或超越性：.1.设F_q是一个有限域，设(a_j)是在F_q\{0}中取值的q-自动机序列，以(a_j)为系数，x作为形式变量的Stieltjes连分式是形式幂级数环F_q[[x]]中元素。我们关心的问题是S(x;a)在F_q(x)上是否是代数的。.2.设(a_j(z))是在F_q[z]\F_q中取值的q-自动机序列。以(a_j(z))作为部分商序列的连分式C(z;a)是形式洛朗级数域F_q((1/z))中元素。我们关心的问题是C(z;a)在F_q(z)上是否是代数的。.我们的目标是给出一些经典的自动机序列定义的连分式和Stieltjes连分式的代数性或超越性的证明，更进一步的目标是给出一个自动机序列定义的连分式是否会是代数的的判据。

This project is about continued fractions and Stieltjes continued fractions in positive characteristic defined by automatic sequences. We are especially interested in the algebraicity or transcendence of such objects:.1. Let F_q be a finite field. Let (a_j) be a q-automatic sequence taking value in F_q\{0}. The Stieltjes continued fraction S(x;a) with (a_j) as the sequence of coefficients and x as formal variable is an element in F_q[[x]]. We want to determine if S(x;a) is algebraic oever F_q(x)..2. Let (a_j(z)) be a q-automatic sequence taking value in F_q[z]\F_q. The continued fraction C(z;a) with the sequence (a_j(z)) as the sequence of partial quotients is then an element in the field of formal Laurent series F_q((1/z)). We want to know if C(z;a) algebraic over F_q(z). .Our goal is to prove the algebraicity or transcendence of continued fractions and Stieltjes continued fraction defined by some classical examples of automatic sequences. Furthermore, we hope to give criteria of automatic sequences that define algebraic continued fractions.