Superposable Trellis Automata

Abstract

A property of superposability is defined here for Treillis Automata as an equivalent of the linearity property of Cellular Automata. We take advantage of the binary local transition function of TAs, which enables us to use an infix notation for it, to study this property in an algebraic framework. We show that a TA is superposable iff its local transition function operates on its set of states as a commutative monoid law and that the general case of commutative monoids is reducible to the case of Abelian groups in which the space-time diagrams obtained are isomorphic to a superposition of figures representing the triangle of binomial coefficients (Pascal's triangle) modulo integers.