Sound and Complete Certificates for Quantitative Termination Analysis of Probabilistic Programs

Abstract We consider the quantitative problem of obtaining lower-bounds on probability termination a given non-deterministic probabilistic program. Specifically, non-termination threshold $$p \in [0, 1],$$ p ∈ [ 0 , 1 ] we aim for certificates proving that program terminates with at least $$1-p$$ - . The basic idea our approach is to find terminating stochastic invariant, i.e. subset $$ SI SI states such (i) ever leaving no more than p , and (ii) almost-surely, either leaves or terminates. While invariants are already well-known, provide first proof above not only sound, but also complete analysis. then introduce novel sound characterization enables template-based approaches easy synthesis certificates, especially in affine polynomial forms. Finally, by combining this existing martingale-based methods relatively qualitative analysis, obtain automated, algorithm Notably, completeness guarantees analysis as strong best-known variant. Our prototype implementation demonstrates effectiveness various programs. demonstrate certifies lower bounds programs beyond reach previous methods.