T-functions revisited: New criteria for bijectivity/transitivity

TL;DR

This paper introduces new criteria for bijectivity and transitivity of T-functions using non-Archimedean ergodic theory and van der Put series, along with a fast evaluation algorithm.

Contribution

It provides novel criteria and an efficient algorithm for analyzing T-functions' bijectivity and transitivity based on $p$-adic analysis.

Findings

New criteria for bijectivity and transitivity of T-functions.

A fast algorithm for evaluating T-functions.

Application of non-Archimedean ergodic theory to T-functions.

Abstract

The paper presents new criteria for bijectivity/transitivity of T-functions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz $p$-adic functions and to study measure-preservation/ergodicity of these.