Tight bounds for the space complexity of nonregular language recognition by real-time machines

TL;DR

This paper investigates the minimal memory requirements for real-time machines recognizing nonregular languages, establishing tight lower bounds and exploring how additional stacks can exponentially reduce space usage.

Contribution

It extends known one-way machine bounds to real-time machines and demonstrates exponential space savings with multiple stacks in real-time pushdown automata.

Findings

Lower bounds for one-way machines are tight for real-time machines.

Increasing stacks in real-time pushdown automata exponentially reduces space.

Memory bounds for nonregular language recognition are established across various machine models.

Abstract

We examine the minimum amount of memory for real-time, as opposed to one-way, computation accepting nonregular languages. We consider deterministic, nondeterministic and alternating machines working within strong, middle and weak space, and processing general or unary inputs. In most cases, we are able to show that the lower bounds for one-way machines remain tight in the real-time case. Memory lower bounds for nonregular acceptance on other devices are also addressed. It is shown that increasing the number of stacks of real-time pushdown automata can result in exponential improvement in the total amount of space usage for nonregular language recognition.