Theory of general linear automata

Linear and affine automata are considered in their general form. The concept of dimensions of a finite automaton is introduced and finite automata of maximal dimensions are shown to be possible. The state reachability problem in monomial form is proved to be undecidable for two-dimensional affine automata. An analogue of Moore's theorem and theorems on homogenous and diagnostic words are also proved. An application of linear automata to mathematical economics is considered. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 10–21, January–February 2009.