R70-44 Synchronization and General Repetitive Machines, with Applications to Ultimate Definite Automata

The authors define a general repetitive machine (GRM) as a finite automaton in which the initial state can be reached from every final state. If there exists a tape which takes all final states to the initial state, the automaton is called a repetitive machine (RM). The RM´s constitute a proper subclass of the GRM´s. The first result is that a GRM is either strongly connected or it has a nonaccepting dead state, and the remaining states form a strongly connected subset.