Time and Space Measures for a Complete Graph Computation Model

TL;DR

This paper introduces a graph-based computation model capable of simulating Turing machines within specific space bounds, using pattern transformations and high-level controls, with comparable efficiency to existing low-level pointer machines.

Contribution

It presents a novel GP 2 graph program model that simulates Turing machines with space complexity O(s(n)) and quadratic time overhead, bridging high-level pattern rules with low-level machine simulation.

Findings

Simulation of Turing machines within space O(s(n))

Quadratic time overhead for the simulation

Comparable properties to storage modification machines

Abstract

We present a computation model based on a subclass of GP 2 graph programs which can simulate any off-line Turing machine of space complexity O(s(n) log s(n)) in space O(s(n)). The simulation only requires a quadratic time overhead. Our model shares this property with Sch\"onhage's storage modification machines and Kolmogorov-Uspenskii machines. These machines use low-level pointer instructions whereas our GP 2-based model uses pattern-based transformation rules and high-level control constructs.