Stable states of asynchronous generator

Asynchronous generators assembled of XOR elements with feedback are under consideration. Such generators are used for random keys production for cryptographic purposes. The goal of the research is to present an analytical procedure for detecting the presence of stable and partly stable states. If the generator is set in one of such states, it stops producing the correct keys. A mathematical model which is based on the theory of linear equations over $GF(2)$ and on the theory of matrices with non-negative elements is suggested. Some examples of implementation of the developed methods are presented.