Thu 11 Jan 2018 14:05 - 14:30 at Bunker Hill - Termination Chair(s): Constantin Enea

Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure) termination problem given a probabilistic program asks whether the program terminates with probability~1. While ranking functions provide a sound and complete method for non-probabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). While deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to academic examples. For non-probabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of real-world programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almost-sure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almost-sure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on abstractions of real-world programs to demonstrate the effectiveness of our approach.

Thu 11 Jan

13:40 - 15:20: Research Papers - Termination at Bunker Hill
Chair(s): Constantin EneaUniversité Paris Diderot
POPL-2018-papers13:40 - 14:05
Annabelle McIverMacquarie University, Carroll MorganUniversity of New South Wales; Data 61, Benjamin Lucien KaminskiRWTH Aachen University; University College London, Joost-Pieter KatoenRWTH Aachen University
POPL-2018-papers14:05 - 14:30
Sheshansh AgrawalIIT Bombay, Krishnendu ChatterjeeIST Austria, Petr NovotnyIST Austria
POPL-2018-papers14:30 - 14:55
Yangjia LiInstitute of Software, Chinese Academy of Sciences, Mingsheng YingUniversity of Technology Sydney
POPL-2018-papers14:55 - 15:20
Ivan RadicekTU Vienna, Gilles BartheIMDEA Software Institute, Marco GaboardiUniversity at Buffalo, SUNY, Deepak GargMax Planck Institute for Software Systems, Florian ZulegerTU Vienna