Multiway Storage Modification Machines

TL;DR

The paper introduces a parallel version of Storage Modification Machines called MWSMM, which recognizes problems in polynomial time similar to Turing Machines in polynomial space, aligning with the Second Machine Class.

Contribution

It presents the MWSMM model, a parallel computational framework that extends existing models and demonstrates its capabilities through a simple implementation.

Findings

MWSMM recognizes problems in polynomial time.

MWSMM aligns with the Second Machine Class.

Implementation of Wolfram's String Substitution System.

Abstract

We present a parallel version of Sch\"onhage's Storage Modification Machine, the Multiway Storage Modification Machine (MWSMM). Like the alternative Association Storage Modification Machine of Tromp and van Emde Boas, MWSMMs recognize in polynomial time what Turing Machines recognize in polynomial space. Falling thus into the Second Machine Class, the MWSMM is a parallel machine model conforming to the Parallel Computation Thesis. We illustrate MWSMMs by a simple implementation of Wolfram's String Substitution System.