Yet another proof of the cascade decomposition theorem for finite automata

We give here a short proof that each finite automaton can be built as a cascade of permutation automata and identity-reset automata.This paper was presented at the Conference on the Algebraic Theory of Machines, Languages and Semigroups, 29 August–8 September 1966, at Asilomar, California, organized by the Krohn-Rhodes Research Institute.