Triangle cellular automata

This paper introduces a special class of cellular automata, called triangle cellular automata, which accept as input strings of length a power of two. In particular, we study the special case in which state information can only move upward through a complete binary tree of finite-state automata. It is shown that this class of cellular automata can accept various string languages in O(log n) time, where n is the length of the input string defining the initial states of the leaf vertices in the tree. Extensions to two dimensions, defining a pyramid cellular automaton, are also given