Systolic trellis automatata †

Abstract

A new type of a systolic automaton, referred to as a systolic trellis automaton, is investigated. It consists of a triangularly shaped system of hexagonally connected processors (functional elements) where the flow of data is uni-directional and there is a fixed delay in all interconnections. Systolic trellis automata can be viewed as a special case of pure systolic systems [3]. Together with systolic tree automata, [6], trellis automata now constitute the most widely studied class of systolic automata, [4],[12]. We describe a variety of programming techniques for trellis automata. The techniques might be of interest for VLSI designers in the sense that a design methodology for VLSI circuits is involved. The power of these techniques is illustrated by several examples. Trellis automata are shown to possess quite surprising 2 capabilities. The languages accepted by trellis automata have time complexity O(n 2)with respect to deterministic Turing machines, and the family of acceptable languages is closed under Boolean operations. Special attention is focused on a subclass of trellis automata with all identical processors, referred to as homogeneous. It has been shown in [2] that the homogeneous trellis automata are exactly equivalent to the real-time one-way cellular automata.