Necks of automata

Milena Bogdanović, Stojan Bogdanović, Miroslav Ćirić, Tatjana Petković

Directable automata, known also as synchronizable, cofinal and reset automata, are a significant type of automata with very interesting algebraic properties and important applications in various branches of Computer Science. They have been a subject of interest of many eminent authors since 1964, when they were introduced by J. Čern\'y in [4], whereas various specializations and generalizations of directable automata have appeared recently, in a paper by T. Petković, M. (Ćirić and S. Bogdanović [7]. The purpose of this paper is to study directable, monogenically and generalized directable automata from another point of view, using the notions of a neck and a local neck that we introduce here.