Preservation of normality by unambiguous transducers

TL;DR

This paper studies how unambiguous finite state transducers preserve Borel normality of sequences, providing an algorithm to decide normality preservation efficiently for strongly connected transducers.

Contribution

It introduces a cubic-time algorithm to determine whether unambiguous transducers preserve normality of infinite sequences.

Findings

Output sequences have block frequencies given by weighted automata.

Normality preservation can be decided efficiently for strongly connected transducers.

The method applies to infinite inputs and outputs, extending previous finite cases.

Abstract

We consider finite state non-deterministic but unambiguous transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality of sequences of symbols. When these transducers are strongly connected, and when the input is a Borel normal sequence, the output is a sequence in which every block has a frequency given by a weighted automaton over the rationals. We provide an algorithm that decides in cubic time whether a unambiguous transducer preserves normality.