Deterministic pushdown automata can compress some normal sequences

TL;DR

This paper demonstrates that deterministic pushdown automata can compress certain normal sequences, providing a positive answer to an open question in the field.

Contribution

It introduces a deterministic pushdown transducer capable of compressing some normal sequences, addressing an open problem from prior research.

Findings

A specific deterministic pushdown transducer compresses a normal sequence.

The result confirms the possibility of compression for some normal sequences.

It resolves an open question in automata-based sequence compression.

Abstract

In this paper, we give a deterministic pushdown transducer and a normal sequence of digits compressed by it. This solves positively a question left open in a previous paper by V. Becher, P. A. Heiber and the first author.