Does a Program Yield the Right Distribution?

Abstract We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. present, to the best of our knowledge, first decidability result for problem determining whether such a program generates exactly specified distribution its outputs (provided terminates almost-surely). The class distributions that can be in formalism consists standard (geometric, uniform, etc.) and finite convolutions thereof. Our method relies on representing these (possibly infinite-support) as probability generating functions which admit effective arithmetic operations. have automated techniques tool called $$\textsc {Prodigy}$$ P R O D I G Y , supports automatic invariance checking, compositional reasoning nested loops, efficient queries output distribution, demonstrated by experiments.