Two-dimensional alternating turing machines

Abstract

This paper introduces a two-dimensional alternating Turing machine (2-ATM) which is an extension of an alternating Turing machine to two-dimensions. This paper also introduces a three-way tiro-dimensional alternating Turing machine (TR2-ATM) which is an alternating version of a three-way two-dimensional Turing machine. We first investigate a relationship between the accepting powers of space-bounded 2-ATM's (or TR2-ATM's) and ordinary space-bounded two-dimansional Turing machines (or three-way two-dimensional Turing machines). We then introduce a simple, natural complexity measure for 2-ATM's (or TR2-ATM's), called "leaf-size", and provides a spectrum of complexity classes based on leaf-size bounded computations. We finally investigate the recognizability of connected patterns by 2-ATM's (or TR2-ATM's).