Generation and analysis of lamplighter programs

TL;DR

This paper introduces a lamplighter group-based programming language, deriving formulas for program enumeration, analyzing growth rates, and exploring random program sampling and runtime distributions.

Contribution

It presents a novel language based on the lamplighter group, with new formulas for counting programs and methods for sampling and analyzing runtimes.

Findings

Derived generating functions and counting formulas for the language.

Established bounds on the growth rate of semantically distinct programs.

Developed a method for sampling random programs and analyzing runtime distributions.

Abstract

We consider a programming language based on the lamplighter group that uses only composition and iteration as control structures. We derive generating functions and counting formulas for this language and special subsets of it, establishing lower and upper bounds on the growth rate of semantically distinct programs. Finally, we show how to sample random programs and analyze the distribution of runtimes induced by such sampling.