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- W2900530797 abstract "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 overapproximate 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." @default.
- W2900530797 created "2018-11-29" @default.
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- W2900530797 date "2018-11-16" @default.
- W2900530797 modified "2023-10-03" @default.
- W2900530797 title "Tail Probabilities for Randomized Program Runtimes via Martingales for Higher Moments" @default.
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- W2900530797 doi "https://doi.org/10.48550/arxiv.1811.06779" @default.
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