Real-time computation by n-dimensional iterative arrays of finite-state machines

An n-dimensional iterative array of finitestate machines (abbreviated nD) is a special type of real-time tape acceptor. The principal results are as follows: 1. nD´s have equivalent forms With simplified stencils and length k encodings of the input alphabet. 2. The set of palindromes and the set of tapes of the form ττ are accepted by 1D´s. 3. The sets of tapes accepted by nD´s are a Boolean algebra. 4. The sets of tapes accepted by nD´s are not closed under multiplication or reflection. 5. There exists a simple phrase-structure language not accepted by any nD in any dimension n. 6. The computing power of the class of nD´s is strictly less than the computing power of the class of (n+1)D´s.