Estimation of the length of reset words for automata with simple idempotents

A quadratic upper bound on the length of a minimal reset word is obtained for finite automata with simple idempotents. Each input symbol of the automata considered induces a transformation that is an idempotent with the unit defect or a bijection on the set of states. This bound is only twice as large as the well-known lower bound of this length. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 32–39, May–June, 2000.