A Computation Model with Automatic Functions and Relations as Primitive Operations

TL;DR

This paper introduces a computational model using automatic functions and relations as primitive operations, demonstrating it remains within polynomial time and analyzing its deterministic and nondeterministic complexities.

Contribution

It proposes a new computation model with automatic functions as primitives, extending previous models while maintaining polynomial time complexity.

Findings

Model covers all primitive operations of prior models.

Remains within polynomial time despite richer primitives.

Analyzes deterministic and nondeterministic complexities of natural problems.

Abstract

Prior work of Hartmanis and Simon (Hartmanis and Simon, 1974) and Floyd and Knuth (Floyd and Knuth, 1990) investigated what happens if a device uses primitive steps more natural than single updates of a Turing tape. One finding was that in the numerical setting, addition, subtraction, comparisons and bit-wise Boolean operations of numbers preserve polynomial time while incorporating concatenation or multiplication allows to solve all PSPACE problems in polynomially many steps. Therefore we propose to use updates and comparisons with automatic functions as primitive operations and use constantly many registers; the resulting model covers all primitive operations of Hartmanis and Simon as well as Floyd and Knuth, but the model remains in polynomial time. The present work investigates in particular the deterministic complexity of various natural problems and also gives an overview on the nondeterministic complexity of this model.