research-article

Open access

Lower Bounds for Possibly Divergent Probabilistic Programs

Authors:

Mingshuai Chen,

Benjamin Lucien Kaminski,

Joost-Pieter Katoen,

Naijun ZhanAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 7, Issue OOPSLA1

Article No.: 99, Pages 696 - 726

https://doi.org/10.1145/3586051

Published: 06 April 2023 Publication History

Abstract

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish non-trivial lower bounds on, e.g., termination probabilities and expected values, for possibly divergent probabilistic loops, e.g., the well-known three-dimensional random walk on a lattice.

References

[1]

Erika Ábrahám, Bernd Becker, Christian Dehnert, Nils Jansen, Joost-Pieter Katoen, and Ralf Wimmer. 2014. Counterexample Generation for Discrete-Time Markov Models: An Introductory Survey. In SFM (LNCS, Vol. 8483). Springer, 65–121.

[2]

Alejandro Aguirre, Gilles Barthe, Justin Hsu, Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Christoph Matheja. 2021. A Pre-Expectation Calculus for Probabilistic Sensitivity. Proc. ACM Program. Lang., 5, POPL (2021), 1–28.

Digital Library

[3]

James Aspnes and Maurice Herlihy. 1990. Fast Randomized Consensus Using Shared Memory. J. Algorithms, 11, 3 (1990), 441–461.

Digital Library

[4]

Philippe Audebaud and Christine Paulin-Mohring. 2009. Proofs of Randomized Algorithms in Coq. Sci. Comput. Program., 74, 8 (2009), 568–589.

Digital Library

[5]

Christel Baier and Joost-Pieter Katoen. 2008. Principles of Model Checking. MIT press.

Digital Library

[6]

Christel Baier, Joachim Klein, Linda Leuschner, David Parker, and Sascha Wunderlich. 2017. Ensuring the Reliability of Your Model Checker: Interval Iteration for Markov Decision Processes. In CAV (II) (LNCS, Vol. 10426). Springer, 160–180.

[7]

Paolo Baldan, Richard Eggert, Barbara König, and Tommaso Padoan. 2021. Fixpoint Theory – Upside Down. In FoSSaCS (LNCS, Vol. 12650). Springer, 62–81.

Digital Library

[8]

Jialu Bao, Nitesh Trivedi, Drashti Pathak, Justin Hsu, and Subhajit Roy. 2022. Data-Driven Invariant Learning for Probabilistic Programs. In CAV (I) (LNCS, Vol. 13371). Springer, 33–54.

[9]

Gilles Barthe, Thomas Espitau, Luis María Ferrer Fioriti, and Justin Hsu. 2016. Synthesizing Probabilistic Invariants via Doob’s Decomposition. In CAV (I) (LNCS, Vol. 9779). Springer, 43–61.

[10]

Gilles Barthe, Thomas Espitau, Benjamin Grégoire, Justin Hsu, and Pierre-Yves Strub. 2018. Proving Expected Sensitivity of Probabilistic Programs. Proc. ACM Program. Lang., 2, POPL (2018), 57:1–57:29.

Digital Library

[11]

Gilles Barthe, Benjamin Grégoire, and Santiago Zanella Béguelin. 2009. Formal Certification of Code-Based Cryptographic Proofs. In POPL. ACM, 90–101.

[12]

Gilles Barthe, Benjamin Grégoire, and Santiago Zanella Béguelin. 2012. Probabilistic Relational Hoare Logics for Computer-Aided Security Proofs. In MPC (LNCS, Vol. 7342). Springer, 1–6.

Digital Library

[13]

2020. Foundations of Probabilistic Programming, Gilles Barthe, Joost-Pieter Katoen, and Alexandra Silva (Eds.). Cambridge University Press.

[14]

Gilles Barthe, Boris Köpf, Federico Olmedo, and Santiago Zanella Béguelin. 2013. Probabilistic Relational Reasoning for Differential Privacy. ACM Trans. Program. Lang. Syst., 35, 3 (2013), 9:1–9:49.

Digital Library

[15]

Ezio Bartocci, Radu Grosu, Panagiotis Katsaros, C. R. Ramakrishnan, and Scott A. Smolka. 2011. Model Repair for Probabilistic Systems. In TACAS (LNCS, Vol. 6605). Springer, 326–340.

[16]

Ezio Bartocci, Laura Kovács, and Miroslav Stankovic. 2019. Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops. In ATVA (LNCS, Vol. 11781). Springer, 255–276.

Digital Library

[17]

Kevin Batz, Mingshuai Chen, Sebastian Junges, Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Christoph Matheja. 2023. Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants. In TACAS. To appear

[18]

Kevin Batz, Mingshuai Chen, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, and Philipp Schröer. 2021. Latticed k-Induction with an Application to Probabilistic Programs. In CAV (I) (LNCS, Vol. 12760). Springer, 524–549.

[19]

Kevin Batz, Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Christoph Matheja. 2021. Relatively Complete Verification of Probabilistic Programs: An Expressive Language for Expectation-Based Reasoning. Proc. ACM Program. Lang., 5, POPL (2021), 1–30.

Digital Library

[20]

Kevin Batz, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, and Thomas Noll. 2019. Quantitative Separation Logic: A Logic for Reasoning about Probabilistic Pointer Programs. Proc. ACM Program. Lang., 3, POPL (2019), 34:1–34:29.

Digital Library

[21]

Daniel Bernoulli. 1954. Exposition of a New Theory on the Measurement of Risk. Econometrica, 22, 1 (1954), 23–36.

[22]

Henrik C. Bohnenkamp, Peter van der Stok, Holger Hermanns, and Frits W. Vaandrager. 2003. Cost-Optimization of the IPv4 Zeroconf Protocol. In DSN. IEEE Computer Society, 531–540.

[23]

Tomás Brázdil, Krishnendu Chatterjee, Martin Chmelik, Vojtech Forejt, Jan Kretínský, Marta Z. Kwiatkowska, David Parker, and Mateusz Ujma. 2014. Verification of Markov Decision Processes Using Learning Algorithms. In ATVA (LNCS, Vol. 8837). Springer, 98–114.

[24]

Michael Carbin, Sasa Misailovic, and Martin C. Rinard. 2016. Verifying Quantitative Reliability for Programs that Execute on Unreliable Hardware. Commun. ACM, 59, 8 (2016), 83–91.

Digital Library

[25]

Aleksandar Chakarov and Sriram Sankaranarayanan. 2013. Probabilistic Program Analysis with Martingales. In CAV (LNCS, Vol. 8044). Springer, 511–526.

[26]

Aleksandar Chakarov and Sriram Sankaranarayanan. 2014. Expectation Invariants for Probabilistic Program Loops as Fixed Points. In SAS (LNCS, Vol. 8723). Springer, 85–100.

[27]

Krishnendu Chatterjee, Hongfei Fu, and Amir Kafshdar Goharshady. 2016. Termination Analysis of Probabilistic Programs Through Positivstellensatz’s. In CAV (I) (LNCS, Vol. 9779). Springer, 3–22.

[28]

Krishnendu Chatterjee, Hongfei Fu, and Petr Novotný. 2020. Termination Analysis of Probabilistic Programs with Martingales. In Foundations of Probabilistic Programming, Gilles Barthe, Joost-Pieter Katoen, and Alexandra Silva (Eds.). Cambridge University Press, 221–258.

[29]

Krishnendu Chatterjee, Hongfei Fu, Petr Novotný, and Rouzbeh Hasheminezhad. 2016. Algorithmic Analysis of Qualitative and Quantitative Termination Problems for Affine Probabilistic Programs. In POPL. ACM, 327–342.

[30]

Krishnendu Chatterjee, Amir Kafshdar Goharshady, Tobias Meggendorfer, and Djordje Zikelic. 2022. Sound and Complete Certificates for Quantitative Termination Analysis of Probabilistic Programs. In CAV (I) (LNCS, Vol. 13371). Springer, 55–78.

[31]

Krishnendu Chatterjee, Petr Novotný, and Dorde Zikelic. 2017. Stochastic Invariants for Probabilistic Termination. In POPL. ACM, 145–160.

[32]

Mingshuai Chen, Joost-Pieter Katoen, Lutz Klinkenberg, and Tobias Winkler. 2022. Does a Program Yield the Right Distribution? Verifying Probabilistic Programs via Generating Functions. In CAV (I) (LNCS, Vol. 13371). Springer, 79–101.

[33]

Yu-Fang Chen, Chih-Duo Hong, Bow-Yaw Wang, and Lijun Zhang. 2015. Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation. In CAV (I) (LNCS, Vol. 9206). Springer, 658–674.

[34]

Fredrik Dahlqvist, Alexandra Silva, and Dexter Kozen. 2020. Semantics of Probabilistic Programming: A Gentle Introduction. In Foundations of Probabilistic Programming, Gilles Barthe, Joost-Pieter Katoen, and Alexandra Silva (Eds.). Cambridge University Press, 1–42.

[35]

Christian Dehnert, Sebastian Junges, Joost-Pieter Katoen, and Matthias Volk. 2017. A Storm is Coming: A Modern Probabilistic Model Checker. In CAV (II) (LNCS, Vol. 10427). Springer, 592–600.

[36]

Edsger Wybe Dijkstra. 1975. Guarded Commands, Nondeterminacy and Formal Derivation of Programs. Commun. ACM, 18, 8 (1975), 453–457.

Digital Library

[37]

Edsger Wybe Dijkstra. 1976. A Discipline of Programming. Prentice-Hall.

Digital Library

[38]

Owain Evans, Andreas Stuhlmüller, John Salvatier, and Daniel Filan. 2017. Modeling Agents with Probabilistic Programs. http://agentmodels.org Accessed: 2022-7-7

[39]

Willliam Feller. 1950. An Introduction to Probability Theory and Its Applications. I, John Wiley & Sons.

[40]

Shenghua Feng, Mingshuai Chen, Han Su, Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Naijun Zhan. 2023. Lower Bounds for Possibly Divergent Probabilistic Programs. CoRR, abs/2302.06082 (2023), arXiv:2302.06082.

[41]

Yijun Feng, Lijun Zhang, David N. Jansen, Naijun Zhan, and Bican Xia. 2017. Finding Polynomial Loop Invariants for Probabilistic Programs. In ATVA (LNCS, Vol. 10482). Springer, 400–416.

[42]

Luis María Ferrer Fioriti and Holger Hermanns. 2015. Probabilistic Termination: Soundness, Completeness, and Compositionality. In POPL. ACM, 489–501.

Digital Library

[43]

Florian Frohn, Matthias Naaf, Marc Brockschmidt, and Jürgen Giesl. 2020. Inferring Lower Runtime Bounds for Integer Programs. ACM Trans. Program. Lang. Syst., 42, 3 (2020), 13:1–13:50.

Digital Library

[44]

Florian Frohn, Matthias Naaf, Jera Hensel, Marc Brockschmidt, and Jürgen Giesl. 2016. Lower Runtime Bounds for Integer Programs. In IJCAR (LNCS, Vol. 9706). Springer, 550–567.

Digital Library

[45]

Hongfei Fu and Krishnendu Chatterjee. 2019. Termination of Nondeterministic Probabilistic Programs. In VMCAI (LNCS, Vol. 11388). Springer, 468–490.

[46]

Jürgen Giesl, Peter Giesl, and Marcel Hark. 2019. Computing Expected Runtimes for Constant Probability Programs. In CADE (LNCS, Vol. 11716). Springer, 269–286.

Digital Library

[47]

Andrew D. Gordon, Thomas A. Henzinger, Aditya V. Nori, and Sriram K. Rajamani. 2014. Probabilistic Programming. In FOSE. ACM, 167–181.

[48]

Marcel Hark, Benjamin Lucien Kaminski, Jürgen Giesl, and Joost-Pieter Katoen. 2019. Aiming Low Is Harder – Inductive Proof Rules for Lower Bounds on Weakest Preexpectations in Probabilistic Program Verification. CoRR, abs/1904.01117 (2019), arXiv:1904.01117.

[49]

Marcel Hark, Benjamin Lucien Kaminski, Jürgen Giesl, and Joost-Pieter Katoen. 2020. Aiming Low Is Harder: Induction for Lower Bounds in Probabilistic Program Verification. Proc. ACM Program. Lang., 4, POPL (2020), 37:1–37:28.

Digital Library

[50]

Arnd Hartmanns and Benjamin Lucien Kaminski. 2020. Optimistic Value Iteration. In CAV (II) (LNCS, Vol. 12225). Springer, 488–511.

Digital Library

[51]

Arnd Hartmanns, Michaela Klauck, David Parker, Tim Quatmann, and Enno Ruijters. 2019. The Quantitative Verification Benchmark Set. In TACAS (I) (LNCS, Vol. 11427). Springer, 344–350.

[52]

Eric Charles Roy Hehner. 2011. A Probability Perspective. Formal Aspects Comput., 23, 4 (2011), 391–419.

Digital Library

[53]

Michael Hicks. 2014. What is Probabilistic Programming? In: The Programming Languages Enthusiast. http://www.pl-enthusiast.net/2014/09/08 Accessed: 2021-12-09

[54]

Chih-Duo Hong, Anthony W. Lin, Rupak Majumdar, and Philipp Rümmer. 2019. Probabilistic Bisimulation for Parameterized Systems - (with Applications to Verifying Anonymous Protocols). In CAV (I) (LNCS, Vol. 11561). Springer, 455–474.

[55]

Jacek Jachymski, Leslaw Gajek, and Piotr Pokarowski. 2000. The Tarski-Kantorovitch Principle and the Theory of Iterated Function Systems. Bulletin of the Australian Mathematical Society, 61, 2 (2000), 247–261.

[56]

Nils Jansen, Christian Dehnert, Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Lukas Westhofen. 2016. Bounded Model Checking for Probabilistic Programs. In ATVA (LNCS, Vol. 9938). 68–85.

[57]

Claire Jones. 1990. Probabilistic Non-determinism. Ph. D. Dissertation. University of Edinburgh, UK.

[58]

Benjamin Lucien Kaminski. 2019. Advanced Weakest Precondition Calculi for Probabilistic Programs. Ph. D. Dissertation. RWTH Aachen University, Germany.

[59]

Benjamin Lucien Kaminski and Joost-Pieter Katoen. 2017. A Weakest Pre-expectation Semantics for Mixed-Sign Expectations. In LICS. IEEE Computer Society, 1–12.

[60]

Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Christoph Matheja. 2019. On the Hardness of Analyzing Probabilistic Programs. Acta Informatica, 56, 3 (2019), 255–285.

Digital Library

[61]

Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, and Federico Olmedo. 2016. Weakest Precondition Reasoning for Expected Run-Times of Probabilistic Programs. In ESOP (LNCS, Vol. 9632). Springer, 364–389.

Digital Library

[62]

Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, and Federico Olmedo. 2018. Weakest Precondition Reasoning for Expected Runtimes of Randomized Algorithms. J. ACM, 65, 5 (2018), 30:1–30:68.

Digital Library

[63]

Joost-Pieter Katoen. 2016. The Probabilistic Model Checking Landscape. In LICS. ACM, 31–45.

[64]

Joost-Pieter Katoen, Friedrich Gretz, Nils Jansen, Benjamin Lucien Kaminski, and Federico Olmedo. 2015. Understanding Probabilistic Programs. In Correct System Design (LNCS, Vol. 9360). Springer, 15–32.

[65]

Joost-Pieter Katoen, Annabelle McIver, Larissa Meinicke, and Carroll C. Morgan. 2010. Linear-Invariant Generation for Probabilistic Programs: Automated Support for Proof-Based Methods. In SAS (LNCS, Vol. 6337). Springer, 390–406.

Digital Library

[66]

Bronisł aw Knaster. 1928. Un Théorème sur les Functions D’ensembles. Annales de la Societe Polonaise de Mathematique, 6 (1928), 133–134.

[67]

Naoki Kobayashi, Ugo Dal Lago, and Charles Grellois. 2020. On the Termination Problem for Probabilistic Higher-Order Recursive Programs. Log. Methods Comput. Sci., 16, 4 (2020).

[68]

Dexter Kozen. 1981. Semantics of Probabilistic Programs. J. Comput. Syst. Sci., 22, 3 (1981), 328–350.

[69]

Dexter Kozen. 1983. A Probabilistic PDL. In STOC. ACM, 291–297.

[70]

Dexter Kozen. 1985. A Probabilistic PDL. J. Comput. Syst. Sci., 30, 2 (1985), 162–178.

[71]

Marta Kwiatkowska, Gethin Norman, and David Parker. 2002. PRISM: Probabilistic Symbolic Model Checker. In TOOLS. Springer, 200–204.

[72]

Marta Z. Kwiatkowska. 2003. Model Checking for Probability and Time: From Theory to Practice. In LICS. IEEE Computer Society, 351.

[73]

Kim Guldstrand Larsen and Arne Skou. 1991. Bisimulation through Probabilistic Testing. Inf. Comput., 94, 1 (1991), 1–28.

Digital Library

[74]

Jean-Louis Lassez, V. L. Nguyen, and E. A. Sonenberg. 1982. Fixed Point Theorems and Semantics: A Folk Tale. Inform. Process. Lett., 14, 3 (1982), 112–116.

[75]

William H. McCrea and Francis J. W. Whipple. 1940. XXII.—Random Paths in Two and Three Dimensions. Proceedings of the Royal Society of Edinburgh, 60, 3 (1940), 281–298.

[76]

Annabelle McIver and Carroll Morgan. 2001. Partial Correctness for Probabilistic Demonic Programs. Theor. Comput. Sci., 266, 1-2 (2001), 513–541.

Digital Library

[77]

Annabelle McIver and Carroll Morgan. 2005. Abstraction, Refinement and Proof for Probabilistic Systems. Springer.

Digital Library

[78]

Annabelle McIver, Carroll Morgan, Benjamin Lucien Kaminski, and Joost-Pieter Katoen. 2018. A New Proof Rule for Almost-Sure Termination. Proc. ACM Program. Lang., 2, POPL (2018), 33:1–33:28.

Digital Library

[79]

Elliot W Montroll. 1956. Random Walks in Multidimensional Spaces, Especially on Periodic Lattices. J. Soc. Indust. Appl. Math., 4, 4 (1956), 241–260.

[80]

Marcel Moosbrugger, Ezio Bartocci, Joost-Pieter Katoen, and Laura Kovács. 2021. The Probabilistic Termination Tool Amber. In FM (LNCS, Vol. 13047). Springer, 667–675.

Digital Library

[81]

Carroll Morgan and Annabelle McIver. 1999. An Expectation-Transformer Model for Probabilistic Temporal Logic. Log. J. IGPL, 7, 6 (1999), 779–804.

[82]

Carroll Morgan, Annabelle McIver, and Karen Seidel. 1996. Probabilistic Predicate Transformers. ACM Trans. Program. Lang. Syst., 18, 3 (1996), 325–353.

Digital Library

[83]

Andrzej S. Murawski and Joël Ouaknine. 2005. On Probabilistic Program Equivalence and Refinement. In CONCUR (LNCS, Vol. 3653). Springer, 156–170.

[84]

Van Chan Ngo, Quentin Carbonneaux, and Jan Hoffmann. 2018. Bounded Expectations: Resource Analysis for Probabilistic Programs. In PLDI. ACM, 496–512.

[85]

Federico Olmedo, Friedrich Gretz, Nils Jansen, Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Annabelle McIver. 2018. Conditioning in Probabilistic Programming. ACM Trans. Program. Lang. Syst., 40, 1 (2018), 4:1–4:50.

Digital Library

[86]

Federico Olmedo, Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Christoph Matheja. 2016. Reasoning about Recursive Probabilistic Programs. In LICS. ACM, 672–681.

[87]

David Park. 1969. Fixpoint Induction and Proofs of Program Properties. Machine Intelligence, 5 (1969).

[88]

G. Pólya. 1921. Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Straßennetz. Math. Ann., 84 (1921), 149–160.

[89]

Tim Quatmann and Joost-Pieter Katoen. 2018. Sound Value Iteration. In CAV (I) (LNCS, Vol. 10981). Springer, 643–661.

[90]

Nasser Saheb-Djahromi. 1978. Probabilistic LCF. In MFCS (LNCS, Vol. 64). Springer, 442–451.

[91]

Sriram Sankaranarayanan. 2020. Quantitative Analysis of Programs with Probabilities and Concentration of Measure Inequalities. In Foundations of Probabilistic Programming, Gilles Barthe, Joost-Pieter Katoen, and Alexandra Silva (Eds.). Cambridge University Press, 259–294.

[92]

Marco Schneider. 1993. Self-Stabilization. ACM Comput. Surv., 25, 1 (1993), 45–67.

Digital Library

[93]

Seyed Mahdi Shamsi, Gian Pietro Farina, Marco Gaboardi, and Nils Napp. 2020. Probabilistic Programming Languages for Modeling Autonomous Systems. In MFI. IEEE, 32–39.

[94]

Marcin Szymczak and Joost-Pieter Katoen. 2019. Weakest Preexpectation Semantics for Bayesian Inference - Conditioning, Continuous Distributions and Divergence. In SETSS (LNCS, Vol. 12154). Springer, 44–121.

[95]

Alfred Tarski. 1955. A Lattice-Theoretical Fixpoint Theorem and Its Applications. Pacific J. Math., 5, 2 (1955), 285–309.

[96]

Jan-Willem van de Meent, Brooks Paige, Hongseok Yang, and Frank Wood. 2018. An Introduction to Probabilistic Programming. CoRR, abs/1809.10756 (2018).

[97]

Di Wang, Jan Hoffmann, and Thomas W. Reps. 2021. Central Moment Analysis for Cost Accumulators in Probabilistic Programs. In PLDI. ACM, 559–573.

[98]

Jinyi Wang, Yican Sun, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar Goharshady. 2021. Quantitative Analysis of Assertion Violations in Probabilistic Programs. In PLDI. ACM, 1171–1186.

[99]

Peixin Wang, Hongfei Fu, Krishnendu Chatterjee, Yuxin Deng, and Ming Xu. 2020. Proving Expected Sensitivity of Probabilistic Programs With Randomized Variable-Dependent Termination Time. Proc. ACM Program. Lang., 4, POPL (2020), 25:1–25:30.

Digital Library

[100]

Peixin Wang, Hongfei Fu, Amir Kafshdar Goharshady, Krishnendu Chatterjee, Xudong Qin, and Wenjun Shi. 2019. Cost Analysis of Nondeterministic Probabilistic Programs. In PLDI. ACM, 204–220.

[101]

David Williams. 1991. Probability with Martingales. Cambridge University Press.

[102]

Mingsheng Ying. 2011. Floyd-Hoare logic for Quantum Programs. ACM Trans. Program. Lang. Syst., 33, 6 (2011), 19:1–19:49.

Digital Library

Cited By

Kura SUnno H(2024)Automated Verification of Higher-Order Probabilistic Programs via a Dependent Refinement Type SystemProceedings of the ACM on Programming Languages10.1145/36746628:ICFP(973-1002)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674662
Gregersen SAguirre AHaselwarter PTassarotti JBirkedal L(2024)Almost-Sure Termination by Guarded RefinementProceedings of the ACM on Programming Languages10.1145/36746328:ICFP(203-233)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674632
Klinkenberg LBlumenthal CChen MHaase DKatoen J(2024)Exact Bayesian Inference for Loopy Probabilistic Programs using Generating FunctionsProceedings of the ACM on Programming Languages10.1145/36498448:OOPSLA1(923-953)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649844
Show More Cited By

Index Terms

Lower Bounds for Possibly Divergent Probabilistic Programs
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic algorithms
    2. Stochastic processes
2. Theory of computation
  1. Semantics and reasoning
    1. Program reasoning

Recommendations

Aiming low is harder: induction for lower bounds in probabilistic program verification

We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to be applied ...
Modular verification for almost-sure termination of probabilistic programs

In this work, we consider the almost-sure termination problem for probabilistic programs that asks whether a given probabilistic program terminates with probability 1. Scalable approaches for program analysis often rely on modularity as their theoretical ...
A Deductive Verification Infrastructure for Probabilistic Programs

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (...

Comments

Information & Contributors

Information

Published In

cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 7, Issue OOPSLA1

April 2023

901 pages

EISSN:2475-1421

DOI:10.1145/3554309

Editor:
Michael Hicks
Amazon, USA

Issue’s Table of Contents

Copyright © 2023 Owner/Author.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 April 2023

Published in PACMPL Volume 7, Issue OOPSLA1

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
354
Total Downloads

Downloads (Last 12 months)259
Downloads (Last 6 weeks)18

Reflects downloads up to 30 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

Kura SUnno H(2024)Automated Verification of Higher-Order Probabilistic Programs via a Dependent Refinement Type SystemProceedings of the ACM on Programming Languages10.1145/36746628:ICFP(973-1002)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674662
Gregersen SAguirre AHaselwarter PTassarotti JBirkedal L(2024)Almost-Sure Termination by Guarded RefinementProceedings of the ACM on Programming Languages10.1145/36746328:ICFP(203-233)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674632
Klinkenberg LBlumenthal CChen MHaase DKatoen J(2024)Exact Bayesian Inference for Loopy Probabilistic Programs using Generating FunctionsProceedings of the ACM on Programming Languages10.1145/36498448:OOPSLA1(923-953)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649844
Zhi DWang PLiu SOng CZhang M(2024)Unifying Qualitative and Quantitative Safety Verification of DNN-Controlled SystemsComputer Aided Verification10.1007/978-3-031-65630-9_20(401-426)Online publication date: 25-Jul-2024
https://doi.org/10.1007/978-3-031-65630-9_20

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents