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Stochastic Invariants for Probabilistic Termination [article]

Krishnendu Chatterjee, Petr Novotný, ore Žikelić
2016 arXiv   pre-print
of termination; (2) repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3) with a combination of ranking and repulsing supermartingales we can establish persistence  ...  Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1) With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability  ...  of termination; (2) repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3) with a combination of ranking and repulsing supermartingales we can establish persistence  ... 
arXiv:1611.01063v2 fatcat:nkhkkxvfavb3hoyd6y4rhhdi5y

Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs [article]

Toru Takisaka, Yuichiro Oyabu, Natsuki Urabe, Ichiro Hasuo
2018 arXiv   pre-print
This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating reachability probabilities.  ...  We give rigorous proofs for their soundness and completeness. We also make an experimental comparison using our implementation of template-based synthesis algorithms for those martingales.  ...  Ranking and Repulsing Supermartingales for Approximating Reachability 9 GiB RAM. That for Prog.  ... 
arXiv:1805.10749v2 fatcat:6jbm445jpnfhnpgvzvmz72mprm

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

Satoshi Kura, Natsuki Urabe, Ichiro Hasuo
2019 Lecture Notes in Computer Science  
Programs with randomization constructs is an active research topic, especially after the recent introduction of martingalebased analysis methods for their termination and runtimes.  ...  To this goal, we devise a theory of supermartingales that overapproximate higher moments of runtime.  ...  We thank the anonymous referees for useful comments.  ... 
doi:10.1007/978-3-030-17465-1_8 fatcat:7bfp3rx2u5a6tcrbmabbmlcln4

Automated Termination Analysis of Polynomial Probabilistic Programs [article]

Marcel Moosbrugger, Ezio Bartocci, Joost-Pieter Katoen, Laura Kovács
2021 arXiv   pre-print
These conditions mostly involve constraints on supermartingales. We consider four proof rules from the literature and extend these with generalizations of existing proof rules for (P)AST.  ...  Experimental results show the merits of our generalized proof rules and demonstrate that Amber can handle probabilistic programs that are out of reach for other state-of-the-art tools.  ...  Both proof rules are based on supermartingales and can certify AST for programs that are not necessarily PAST.  ... 
arXiv:2010.03444v3 fatcat:u4v3xuydc5bw3eun3h47pwklxy

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.  ...  To this goal, we devise a theory of supermartingales that overapproximate higher moments of runtime.  ...  We thank the anonymous referees for useful comments.  ... 
arXiv:1811.06779v2 fatcat:lgchqbavufc6flxo6nn5tlp37q

Learning Probabilistic Termination Proofs [chapter]

Alessandro Abate, Mirco Giacobbe, Diptarko Roy
2021 Lecture Notes in Computer Science  
Ranking supermartingales (RSMs) prove that probabilistic programs halt, in expectation, within a finite number of steps.  ...  We introduce the neural ranking supermartingale: we let a neural network fit an RSM over execution traces and then we verify it over the source code using satisfiability modulo theories (SMT); if the latter  ...  Our method addresses the PAST question only, by building upon the theory of ranking supermartingales [10] . Ranking Supermartingales.  ... 
doi:10.1007/978-3-030-81688-9_1 fatcat:srgow3ul6ncypi5hkzdiwstovq

Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants [article]

Kevin Batz, Mingshuai Chen, Sebastian Junges, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja
2022 arXiv   pre-print
We contribute an inductive synthesis approach for proving quantitative reachability properties by finding inductive invariants on source-code level.  ...  and often outperforming monolithic alternatives.  ...  Two notable exceptions to literature focussing on almost-sure termination are: (1) ε-decreasing supermartingales [15, 16] and (2) nonnegative repulsing supermartingales [49] ; both can upper-bound arbitrary  ... 
arXiv:2205.06152v1 fatcat:fx27zel32bhfnkd24zj5ajrgpi

Automating termination analysis of probabilistic programs

Marcel Moosbrugger, Laura Kovacs
2020
For certifying the negation of almost-sure termination, we generalize existing proof rules involving repulsing supermartingales, to handle unbounded polynomial variable updates of programs.  ...  We establish incomplete but sound algorithms for almost-sure termination, positive-almost-sure termination, and the negations thereof.  ...  [CNZ17], which introduced repulsing supermartingales and stochastic invariants, also provided an algorithmic approach for constructing linear repulsing supermartingales for a stochastic invariant.  ... 
doi:10.34726/hss.2020.77501 fatcat:adop6b7kvbfyve3wbkg5bx57da

Proceedings of the 2022 Joint Workshop of the German Research Training Groups in Computer Science

Felix Freiling, Helmut Seidl, 2022 2022 Joint Workshop Of The German Research Training Groups In Computer Science June 12–June 15
2022
The meeting featured the usual sequence of research presentations by funded researchers, networking meetings for PIs and RTG coordinators, as well as two invited talks, one by Professor Martina Seidl (  ...  Informatics, one of the world's premier venues for computer science-related seminars.  ...  Probabilistic ranking functions, a variant of ranking functions adapted for probabilistic programs based on the theory of ranking supermartingales 1 (RSM), present a natural way to obtain bounds on the  ... 
doi:10.25593/opus4-fau-19321 fatcat:ry4vd32xxbgldirrvymuaxxqwi