Some regular state sets in the system of one-dimensional iterative automata

Abstract

For the system of one-dimensional iterative automata, each set of all passive, Garden-of-Eden, and branching point state configurations is defined and shown to constitute a regular set. This regularity is proved to hold for the fixed, cyclic, open and reflexive boundary conditions. For proving theorems, a new device called N-automaton is introduced. Relationship with the gsm mapping is also discussed.