Complex Systems

A Note on Injectivity of Additive Cellular Automata Download PDF

Burton Voorhees
Faculty of Science, Athabasca University,
Box 10,000, Athabasca, Alberta T0G 2R0, Canada


Additive cellular automata on finite sequences with periodic boundary conditions are treated in terms of complex polynomials whose arguments are roots of unity. It is shown that the condition for a binary one-dimensional additive cellular automaton to be injective is that the associated complex polynomial have no zeros that are roots of unity.