Tail Probabilities for Randomized Program Runtimes via Martingales for Higher Moments [article]

Satoshi Kura, Natsuki Urabe, Ichiro Hasuo
2019 arXiv   pre-print
Programs with randomization constructs is an active research topic, especially after the recent introduction of martingale-based analysis methods for their termination and runtimes. Unlike most of the existing works that focus on proving almost-sure termination or estimating the expected runtime, in this work we study the tail probabilities of runtimes-such as "the execution takes more than 100 steps with probability at most 1%." To this goal, we devise a theory of supermartingales that
more » ... oximate higher moments of runtime. These higher moments, combined with a suitable concentration inequality, yield useful upper bounds of tail probabilities. Moreover, our vector-valued formulation enables automated template-based synthesis of those supermartingales. Our experiments suggest the method's practical use.
arXiv:1811.06779v2 fatcat:lgchqbavufc6flxo6nn5tlp37q