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Stochastic Invariants for Probabilistic Termination
[article]
2016
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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]
2019
Lecture Notes in Computer Science
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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]
2021
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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]
2021
Lecture Notes in Computer Science
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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]
2022
arXiv
pre-print
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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
2020
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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
2022
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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