T-functions revisited: New criteria for bijectivity/transitivity

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.

References in corpus (3)

• Non-Archimedean Ergodic Theory and Pseudorandom Generators
• Automata finiteness criterion in terms of van der Put series of automata functions
• Ergodic Theory Over ${\F}_2[[T]]$

Cited by in corpus (6)

• $p$-Adic Mathematical Physics: The First 30 Years
• Ergodicity criteria for non-expanding transformations of 2-adic spheres
• Criteria of ergodicity for $p$-adic dynamical systems in terms of coordinate functions
• Ergodic dynamical systems over the Cartesian power of the ring of p-adic integers
• On the bijective colouring of Cantor trees based on transducers
• A new class of $p$-adic Lipschitz functions and multidimensional Hensel's Lemma