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.
['Stephen N. Cole']
Real-time computation by n-dimensional iterative arrays of finite-state machines