Tail-Bound Cost Analysis over Nondeterministic Probabilistic Programs - Wang, Peixin (Shanghai jiao tong da xue xue bao, 2023)
For probabilistic programs, there is some work for qualitative and quantitative analysis about expectation or mean, such as expected termination time, and expected cost analysis. However, another non-trivial issue is about tail bounds (i.e., upper bounds of tail probabilities), which can provide high-probability guarantees to extreme events. In this work, we focus on the problem of tail-bound cost analysis over nondeterministic probabilistic programs, which aims to automatically obtain the tail bound of resource usages over such programs. To achieve this goal, we present a novel approach, combined with a suitable concentration inequality, to derive the tail bound of accumulated cost until program termination. Our approach can handle both positive and negative costs. Moreover, our approach enables an automated template-based synthesis of supermartingales and leads to an efficient polynomial-time algorithm. To show the effectiveness of our approach, we present experimental results on various programs and make a comparison with state-of-the-art tools.