Generation and analysis of lamplighter programs

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.

Added section 7 (sampling random programs) and section 8 (distribution of runtimes)