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J.A. Brzozowski, Dept. of Appl. Analysis and Computer Sci. University of Waterloo
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.
Citation:
J.A. Brzozowski, "R70-44 Synchronization and General Repetitive Machines, with Applications to Ultimate Definite Automata," IEEE Transactions on Computers, vol. 19, no. 10, pp. 989-990, Oct. 1970, doi:10.1109/T-C.1970.222817
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