R70-14 Some Results on Cascade Decomposition of Automata

The automaton decomposition procedure described by Zeiger1 does not necessarily yield a unique cascade decomposition of a given machine M. This paper describes some characteristics of the machines in any such decomposition of M which may be predicted by examining states of M that are permuted under some input sequence x. The principal results fall into three main categories: cascade consequences of tapes which permute proper subsets of QM, the sate set of M; consequences of symbols which permute QM; and the decomposition of definite automata.