Sequential Machine Characterizations of Trellis and Cellular Automata and Applications

Abstract

We look at a simple, but general model, of a systolic system called a trellis automaton (TA). A TA is equivalent in computational power to a one-dimensional unbounded cellular automaton (CA), a model of parallel computation which has been studied extensively in the literature. Different varieties of TA’s are equivalent to corresponding variations of CA’s. We present, for the first time, sequential machine characterizations of TA’s (CA’s). The sequential machines are useful and powerful tools for investigating properties of TA’s (CA’s). They ar easy to program because, unlike the parallel models, one does not have to deal with the problem of synchronization. Several applications are given. In particular, we prove a new speed-up theorem which is stronger than what has previously been shown.