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Deterministic pushdown automata can compress some normal sequences

Olivier Carton, Sylvain Perifel

TL;DR

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

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.

Deterministic pushdown automata can compress some normal sequences

TL;DR

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

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.
Paper Structure (4 sections, 6 theorems, 7 equations, 1 figure, 1 table)

This paper contains 4 sections, 6 theorems, 7 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Precise statement
  3. Proof
  4. Acknowledgements.

Key Result

Theorem 1.1

There is a deterministic one-to-one pushdown transducer that can compress some normal sequence.

Figures (1)

  • Figure 1: Example of a function $f$: $f(3) = 14$.

Theorems & Definitions (10)

  • Theorem 1.1
  • Proposition 2.1
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • proof : Proof of Proposition \ref{['pro:formal']}