Uniform generation of large traces

TL;DR

This paper presents an algorithm for the uniform generation of infinite traces, allowing effective on-the-fly approximation with different trade-offs between computational cost and speed.

Contribution

It introduces two novel algorithms for uniform generation of infinite traces, balancing computational efficiency and production speed, with specific optimizations for certain trace monoids.

Findings

The algorithm's approximation size grows linearly with execution time.

Two algorithm variants offer different trade-offs between speed and computational cost.

For some trace monoids, the algorithms are highly efficient with minimal computations.

Abstract

We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed according to the exact uniform probability measure. The average size of the approximation grows linearly with the time of execution of the algorithm, hence its output can be effectively used while running. Two versions of the algorithm are given. A version without rejection has a good production speed, provided that some precomputations have been done, but these may be costly. A version with rejection requires much fewer computations, at the expense of a production speed that can be small. We also show that, for some particular trace monoids, one or the other version of the algorithm can actually be very good: few computations for a good production speed.