Time-Reversible Random Number Generators : Solution of Our Challenge by Federico Ricci-Tersenghi

TL;DR

This paper discusses the concept of time-reversible random number generators, illustrating how they can be constructed and providing a reversed version of a pseudorandom generator as a solution to the challenge.

Contribution

It introduces the idea of time-reversible random number generators and presents a reversed version of a pseudorandom generator as a novel solution.

Findings

Reversed pseudorandom number generator demonstrated

Time-reversibility achieved in stochastic algorithms

Provides a method to store and reverse pseudorandom sequences

Abstract

Nearly all the evolution equations of physics are time-reversible, in the sense that a movie of the solution, played backwards, would obey exactly the same differential equations as the original forward solution. By way of contrast, stochastic approaches are typically not time-reversible, though they could be made so by the simple expedient of storing their underlying pseudorandom numbers in an array. Here we illustrate the notion of time-reversible random number generators. In Version 1 we offered a suitable reward for the first arXiv response furnishing a reversed version of an only slightly-more-complicated pseudorandom number generator. Here we include Professor Ricci-Tersenghi's prize-winning reversed version as described in his arXiv:1305.1805 contribution: "The Solution to the Challenge in `Time-Reversible Random Number Generators' by Wm. G. Hoover and Carol G. Hoover".