Learning Probabilistic Termination Proofs

Abstract We present the first machine learning approach to termination analysis of probabilistic programs. Ranking supermartingales (RSMs) prove that programs halt, in expectation, within a finite number steps. While previously RSMs were directly synthesised from source code, our method learns them sampled execution traces. introduce neural ranking supermartingale : we let network fit an RSM over traces and then verify it code using satisfiability modulo theories (SMT); if latter step produces counterexample, generate new sample repeat counterexample-guided inductive synthesis loop, until SMT solver confirms validity RSM. The result is thus sound witness termination. Our strategy agnostic its verification counterpart supports widest range single-loop any existing tool can handle date. demonstrate efficacy benchmarks include linear polynomial with discrete, continuous, state-dependent, multi-variate, hierarchical distributions, distributions undefined moments.