COOPERATING SYSTEMS OF THREE-WAY, TWO-DIMENSIONAL FINITE AUTOMATA

Abstract

This paper introduces a cooperating system of three-way, two-dimensional finite automata (CS-TR2-FA) which is a restricted version of a cooperating system of four- way, two-dimensional finite automata (CS-2-FA), and mainly investigates several fundamental properties of this system as a two-dimensional language acceptor whose input tapes are restricted to square ones. We show that (1) CS-TR2-FA’s are equivalent in accepting power to three-way, two-dimensional simple multihead finite automata, (2) CS-2-FA’s are more powerful than CS-TR2-FA’s, (3) £[CS-TR2-DFA(k)S] ⊊ £[CS-TR2-NFA(k)S], (4) ⋃1≤k<∞ £[CS-TR2-DFA(k)S] ⊊ ⋃1≤k<∞ £[CS-TR2-NFA(k)S], and (5) £[CS-TR2-DFA(k)S] (£[CS-TR2-NFA(k)S]) ⊊ £[CS-TR2-DFA(k+1)S] (£[CS-TR2-NFA(k+1)S]), where £[CS-TR2-DFA(k)S] (£[CS-TR2-NFA(k)S]) denotes the class of sets of square input tapes accepted by CS-TR2-FA’s which consist of k deterministic (non-deterministic) finite automata.