Abstract
The study is focused on a problem of accumulating information with finite automata. Potentially infinite input data with a given structure and exhibiting possible irregularities and abnormalities are considered. Irregularities are acceptable exceptions of the given structure while abnormalities are unacceptable exceptions of this structure. In the paper, analysis of irregularities and abnormalities with usage of different types of finite automata are illustrated. We start with classical deterministic and nondeterministic finite automata. Then, a description of classical finite automata are generalized in terms of imperfectness of transition function and input data. The aim of this "work in progress" paper is just examples based illustration of different types of finite automata applied to potentially infinite time series like input data. Presented examples offer some illustrative proposals of farther research.