This is the moment for probabilistic loops

We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on externally provided invariants or templates. We employ algebrai...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of ACM on programming languages Jg. 6; H. OOPSLA2; S. 1497 - 1525
Hauptverfasser: Moosbrugger, Marcel, Stankovič, Miroslav, Bartocci, Ezio, Kovács, Laura
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY, USA ACM 31.10.2022
Schlagworte:
Computing methodologies
Markov processes
Mathematics of computing
Random walks and Markov chains
Symbolic and algebraic algorithms
Theory of computation
Higher Moments
Distribution Recovery
Linear Recurrences
Probabilistic Programs
ISSN:2475-1421, 2475-1421
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on externally provided invariants or templates. We employ algebraic techniques based on linear recurrences and introduce program transformations to simplify probabilistic programs while preserving their statistical properties. We develop power reduction techniques to further simplify the polynomial arithmetic of probabilistic programs and define the theory of moment-computable probabilistic loops for which higher moments can precisely be computed. Our work has applications towards recovering probability distributions of random variables and computing tail probabilities. The empirical evaluation of our results demonstrates the applicability of our work on many challenging examples.
AbstractList We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on externally provided invariants or templates. We employ algebraic techniques based on linear recurrences and introduce program transformations to simplify probabilistic programs while preserving their statistical properties. We develop power reduction techniques to further simplify the polynomial arithmetic of probabilistic programs and define the theory of moment-computable probabilistic loops for which higher moments can precisely be computed. Our work has applications towards recovering probability distributions of random variables and computing tail probabilities. The empirical evaluation of our results demonstrates the applicability of our work on many challenging examples.
ArticleNumber 178
Author Bartocci, Ezio
Moosbrugger, Marcel
Kovács, Laura
Stankovič, Miroslav
Author_xml – sequence: 1
  givenname: Marcel
  orcidid: 0000-0002-2006-3741
  surname: Moosbrugger
  fullname: Moosbrugger, Marcel
  email: marcel.moosbrugger@tuwien.ac.at
  organization: TU Wien, Austria
– sequence: 2
  givenname: Miroslav
  orcidid: 0000-0001-5978-7475
  surname: Stankovič
  fullname: Stankovič, Miroslav
  email: miroslav.stankovic@tuwien.ac.at
  organization: TU Wien, Austria
– sequence: 3
  givenname: Ezio
  orcidid: 0000-0002-8004-6601
  surname: Bartocci
  fullname: Bartocci, Ezio
  email: ezio.bartocci@tuwien.ac.at
  organization: TU Wien, Austria
– sequence: 4
  givenname: Laura
  orcidid: 0000-0002-8299-2714
  surname: Kovács
  fullname: Kovács, Laura
  email: laura.kovacs@tuwien.ac.at
  organization: TU Wien, Austria
BookMark eNptj81LAzEUxINUsNbi3dPeBGFtXpLdbI5S_IJCL_W8vKQJjexuliQX_3tXWkVEGHgD82Mec0lmQxgsIddA7wFEteJVzbmAMzJnQlYlCAazX_6CLFN6p5SC4qLhak7udgefikn5YIs-9HbIhQuxGGPQqH3nU_am6EIY0xU5d9gluzzdBXl7etytX8rN9vl1_bApkUmZS0XBYSOclQwVColOuukdtcBAirrRU6JtrZV0TjNjasUaqUGqPZhqzy1fkNtjr4khpWhdO0bfY_xogbZfK9vTyoks_5DGZ8w-DDmi7_7hb448mv6n9Dv8BF3OW8M
CitedBy_id crossref_primary_10_1145_3632905
crossref_primary_10_1145_3704894
crossref_primary_10_1145_3704874
crossref_primary_10_1145_3728648
crossref_primary_10_1145_3586050
crossref_primary_10_1007_s10703_024_00455_0
crossref_primary_10_1145_3641545
crossref_primary_10_1145_3632872
crossref_primary_10_1145_3649822
crossref_primary_10_1145_3649844
Cites_doi 10.1007/978-3-030-81688-9_25
10.1038/261459a0
10.1007/978-3-319-46520-3_30
10.1007/978-3-7091-0445-3
10.1007/978-3-642-40196-1_17
10.1007/978-3-319-29604-3_5
10.1145/2491411.2491423
10.1145/3428208
10.1007/978-3-319-10936-7_6
10.3929/ETHZ-A-001631582
10.1145/3087604.3087623
10.1007/0-387-32227-2
10.1016/j.ic.2006.05.002
10.1007/s00165-012-0227-6
10.1145/3453483.3454062
10.1007/978-3-030-17465-1_8
10.1007/978-3-031-13185-1_3
10.1145/3158142
10.1145/3290368
10.1016/j.peva.2010.04.001
10.1145/3385412.3386035
10.1145/195613.195632
10.1063/1.5125097
10.1007/978-3-030-81688-9_27
10.1145/3385412
10.1007/978-3-662-49674-9_13
10.1007/978-3-662-49498-1
10.1145/1005285.1005324
10.1145/2103656.2103670
10.1007/978-3-540-78800-3_18
10.1007/978-3-319-41528-4_3
10.1007/978-3-319-63390-9
10.1007/978-3-319-41528-4_4
10.1038/nature14541
10.1007/978-3-030-64276-1
10.1109/FMCAD.2015.7542253
10.1007/978-3-319-68167-2_26
10.1007/978-3-642-15769-1_24
10.1017/9781108770750
10.1145/3453483.3454078
10.1016/j.tcs.2021.12.021
10.1007/b138392
10.1016/0022-0000(85)90012-1
10.1007/978-3-642-22110-1
10.1109/IROS45743.2020.9340755
10.1109/CDC.2015.7403319
10.1007/978-3-319-21690-4
10.1093/acprof:oso/9780199535255.001.0001
10.1016/0020-0190(90)90107-9
10.1017/cbo9780511814075
10.1007/978-3-319-73721-8_11
10.1017/9781108591034
10.1080/01621459.1965.10480775
10.1007/978-3-030-31784-3_15
10.2307/2334940
10.1007/s00236-018-0321-1
10.1007/978-3-642-31113-0
10.1007/978-3-030-45190-5_28
10.5281/zenodo.7055030
ContentType Journal Article
Copyright Owner/Author
Copyright_xml – notice: Owner/Author
DBID AAYXX
CITATION
DOI 10.1145/3563341
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 2475-1421
EndPage 1525
ExternalDocumentID 10_1145_3563341
3563341
GrantInformation_xml – fundername: Vienna Science and Technology Fund
  grantid: ICT19-018
  funderid: http://dx.doi.org/10.13039/501100001821
– fundername: Austrian Science Fund
  grantid: W1255-N23
  funderid: http://dx.doi.org/10.13039/501100002428
– fundername: European Research Council
  grantid: 101002685
  funderid: http://dx.doi.org/10.13039/501100000781
GroupedDBID AAKMM
AAYFX
ACM
ADPZR
AIKLT
ALMA_UNASSIGNED_HOLDINGS
GUFHI
LHSKQ
M~E
OK1
ROL
AAYXX
AEFXT
AEJOY
AKRVB
CITATION
ID FETCH-LOGICAL-a277t-901fa84fe72a9a47af7f1930e1217468bfe7be6b97ffb2cc69287b179d1c5d3e3
ISICitedReferencesCount 17
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001083750200055&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2475-1421
IngestDate Sat Nov 29 07:46:47 EST 2025
Tue Nov 18 22:04:26 EST 2025
Mon Feb 24 21:14:28 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue OOPSLA2
Keywords Higher Moments
Distribution Recovery
Linear Recurrences
Probabilistic Programs
Language English
License This work is licensed under a Creative Commons Attribution 4.0 International License.
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-a277t-901fa84fe72a9a47af7f1930e1217468bfe7be6b97ffb2cc69287b179d1c5d3e3
ORCID 0000-0002-8299-2714
0000-0002-2006-3741
0000-0002-8004-6601
0000-0001-5978-7475
OpenAccessLink https://dl.acm.org/doi/10.1145/3563341
PageCount 29
ParticipantIDs crossref_primary_10_1145_3563341
crossref_citationtrail_10_1145_3563341
acm_primary_3563341
PublicationCentury 2000
PublicationDate 2022-10-31
PublicationDateYYYYMMDD 2022-10-31
PublicationDate_xml – month: 10
  year: 2022
  text: 2022-10-31
  day: 31
PublicationDecade 2020
PublicationPlace New York, NY, USA
PublicationPlace_xml – name: New York, NY, USA
PublicationTitle Proceedings of ACM on programming languages
PublicationTitleAbbrev ACM PACMPL
PublicationYear 2022
Publisher ACM
Publisher_xml – name: ACM
References Guillaume Claret, Sriram K. Rajamani, Aditya V. Nori, Andrew D. Gordon, and Johannes Borgström. 2013. Bayesian Inference Using Data Flow Analysis. In Proc. of ESEC/FSE. https://doi.org/10.1145/2491411.2491423 10.1145/2491411.2491423
Zachary Kincaid, John Cyphert, Jason Breck, and T. Reps. 2018. Non-Linear Reasoning for Invariant Synthesis. In Proc. of POPL. https://doi.org/10.1145/3158142 10.1145/3158142
Feras A. Saad, Martin C. Rinard, and Vikash K. Mansinghka. 2021. SPPL: Probabilistic Programming With Fast Exact Symbolic Inference. In Proc. of PLDI. https://doi.org/10.1145/3453483.3454078 10.1145/3453483.3454078
Dominik Gruntz. 1996. On Computing Limits in a Symbolic Manipulation System. Ph. D. Dissertation. ETH Zürich. https://doi.org/10.3929/ETHZ-A-001631582 10.3929/ETHZ-A-001631582
Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady, and Ehsan Kafshdar Goharshady. 2020. Polynomial Invariant Generation for Non-deterministic Recursive Programs. In Proc. of PLDI. https://doi.org/10.1145/3385412 10.1145/3385412
Manuel Kauers and Peter Paule. 2011. The Concrete Tetrahedron - Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates. Springer. https://doi.org/10.1007/978-3-7091-0445-3 10.1007/978-3-7091-0445-3
Rajeev Motwani and Prabhakar Raghavan. 1995. Randomized Algorithms. Cambridge University Press. https://doi.org/10.1017/cbo9780511814075 10.1017/cbo9780511814075
Zachary Kincaid, Jason Breck, John Cyphert, and T. Reps. 2019. Closed Forms for Numerical Loops. In Proc. of POPL. https://doi.org/10.1145/3290368 10.1145/3290368
Praveena Narayanan, Jacques Carette, Wren Romano, Chung chieh Shan, and Robert Zinkov. 2016. Probabilistic Inference by Program Transformation in Hakaru (System Description). In Proc. of FLOPS. https://doi.org/10.1007/978-3-319-29604-3_5 10.1007/978-3-319-29604-3_5
Gilles Barthe, Thomas Espitau, Luis María Ferrer Fioriti, and Justin Hsu. 2016. Synthesizing Probabilistic Invariants via Doob’s Decomposition. In Proc. of CAV. https://doi.org/10.1007/978-3-319-41528-4_3 10.1007/978-3-319-41528-4_3
Yi Chou, Hansol Yoon, and Sriram Sankaranarayanan. 2020. Predictive Runtime Monitoring of Vehicle Models Using Bayesian Estimation and Reachability Analysis. In Proc. of IROS. https://doi.org/10.1109/IROS45743.2020.9340755 10.1109/IROS45743.2020.9340755
Konstantin Selyunin, Denise Ratasich, Ezio Bartocci, Md. Ariful Islam, Scott A. Smolka, and Radu Grosu. 2015. Neural Programming: Towards Adaptive Control in Cyber-Physical Systems. In Proc. of CDC. https://doi.org/10.1109/CDC.2015.7403319 10.1109/CDC.2015.7403319
Steven de Oliveira, Saddek Bensalem, and Virgile Prevosto. 2016. Polynomial Invariants by Linear Algebra. In Proc. of ATVA. https://doi.org/10.1007/978-3-319-46520-3_30 10.1007/978-3-319-46520-3_30
Ezio Bartocci, Laura Kovács, and Miroslav Stankovic. 2020. Analysis of Bayesian Networks via Prob-Solvable Loops. In Proc. of ICTAC. https://doi.org/10.1007/978-3-030-64276-1 10.1007/978-3-030-64276-1
Steven Holtzen, Guy Van den Broeck, and Todd D. Millstein. 2020. Scaling Exact Inference for Discrete Probabilistic Programs. In Proc. of OOPSLA. https://doi.org/10.1145/3428208 10.1145/3428208
Andreas Humenberger, Maximilian Jaroschek, and Laura Kovács. 2017. Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences. In Proc. of ISSAC. https://doi.org/10.1145/3087604.3087623 10.1145/3087604.3087623
Wilfred K. Hastings. 1970. Monte Carlo Sampling Methods Using Markov Chains and Their Applications. Biometrika, https://doi.org/10.2307/2334940 10.2307/2334940
Steven Holtzen, Sebastian Junges, Marcell Vazquez-Chanlatte, Todd D. Millstein, Sanjit A. Seshia, and Guy Van den Broeck. 2021. Model Checking Finite-Horizon Markov Chains with Probabilistic Inference. In Proc. of CAV. https://doi.org/10.1007/978-3-030-81688-9_27 10.1007/978-3-030-81688-9_27
Annabelle McIver and Carroll Morgan. 2005. Abstraction, Refinement and Proof for Probabilistic Systems. Springer. https://doi.org/10.1007/b138392 10.1007/b138392
Stanley L. Warner. 1965. Randomized Response: A Survey Technique for Eliminating Evasive Answer Bias. J. Am. Stat. Assoc., https://doi.org/10.1080/01621459.1965.10480775 10.1080/01621459.1965.10480775
Azadeh Farzan and Zachary Kincaid. 2015. Compositional Recurrence Analysis. In Proc. of FMCAD. https://doi.org/10.1109/FMCAD.2015.7542253 10.1109/FMCAD.2015.7542253
Jason Breck, John Cyphert, Zachary Kincaid, and Thomas W. Reps. 2020. Templates and Recurrences: Better Together. In Proc. of PLDI. https://doi.org/10.1145/3385412.3386035 10.1145/3385412.3386035
Christian Dehnert, Sebastian Junges, Joost-Pieter Katoen, and Matthias Volk. 2017. A Storm is Coming: A Modern Probabilistic Model Checker. In Proc. of CAV. https://doi.org/10.1007/978-3-319-63390-9 10.1007/978-3-319-63390-9
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 Proc. of CAV. https://doi.org/10.1007/978-3-030-81688-9_25 10.1007/978-3-030-81688-9_25
Håkan L. S. Younes and Reid G. Simmons. 2006. Statistical probabilistic model checking with a focus on time-bounded properties. Inf. Comput., https://doi.org/10.1016/j.ic.2006.05.002 10.1016/j.ic.2006.05.002
Olivier Bouissou, Eric Goubault, Sylvie Putot, Aleksandar Chakarov, and Sriram Sankaranarayanan. 2016. Uncertainty Propagation Using Probabilistic Affine Forms and Concentration of Measure Inequalities. In Proc. of TACAS. https://doi.org/10.1007/978-3-662-49674-9_13 10.1007/978-3-662-49674-9_13
Richard M. Karp. 1994. Probabilistic Recurrence Relations. J. ACM, https://doi.org/10.1145/195613.195632 10.1145/195613.195632
Milton F. Maritz. 2020. A Note on Exact Solutions of the Logistic Map. Chaos: An Interdisciplinary Journal of Nonlinear Science, https://doi.org/10.1063/1.5125097 10.1063/1.5125097
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 Proc. of SAS. https://doi.org/10.1007/978-3-642-15769-1_24 10.1007/978-3-642-15769-1_24
Aleksandar Chakarov and Sriram Sankaranarayanan. 2014. Expectation Invariants for Probabilistic Program Loops as Fixed Points. In Proc. of SAS. https://doi.org/10.1007/978-3-319-10936-7_6 10.1007/978-3-319-10936-7_6
Dexter Kozen. 1985. A Probabilistic PDL. J. Comput. System Sci., https://doi.org/10.1016/0022-0000(85)90012-1 10.1016/0022-0000(85)90012-1
Marta Z. Kwiatkowska, Gethin Norman, and David Parker. 2011. PRISM 4.0: Verification of Probabilistic Real-Time Systems. In Proc. of CAV. https://doi.org/10.1007/978-3-642-22110-1 10.1007/978-3-642-22110-1
Marcel Moosbrugger, Miroslav Stankovič, Ezio Bartocci, and Laura Kovács. 2022. This is the Moment for Probabilistic Loops - Artifact (Polar). https://doi.org/10.5281/zenodo.7055030 10.5281/zenodo.7055030
Yu-Fang Chen, Chih-Duo Hong, Bow-Yaw Wang, and Lijun Zhang. 2015. Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation. In Proc. of CAV. https://doi.org/10.1007/978-3-319-21690-4 10.1007/978-3-319-21690-4
Rick Durrett. 2019. Probability: Theory and Examples. Cambridge University Press. https://doi.org/10.1017/9781108591034 10.1017/9781108591034
Timon Gehr, Sasa Misailovic, and Martin T. Vechev. 2016. PSI: Exact Symbolic Inference for Probabilistic Programs. In Proc. of CAV. https://doi.org/10.1007/978-3-319-41528-4_4 10.1007/978-3-319-41528-4_4
Laura Kovács. 2008. Reasoning Algebraically About P-Solvable Loops. In Proc. of TACAS. https://doi.org/10.1007/978-3-540-78800-3_18 10.1007/978-3-540-78800-3_18
Gilles Barthe, Boris Köpf, Federico Olmedo, and Santiago Zanella Béguelin. 2012. Probabilistic Relational Reasoning for Differential Privacy. In Proc. of POPL. https://doi.org/10.1145/2103656.2103670 10.1145/2103656.2103670
John E. Kolassa. 2006. Series Approximation Methods in Statistics. Springer. https://doi.org/10.1007/0-387-32227-2 10.1007/0-387-32227-2
Miroslav Stankovic, Ezio Bartocci, and Laura Kovács. 2022. Moment-Based Analysis of Bayesian Network Properties. Theor. Comput. Sci., https://doi.org/10.1016/j.tcs.2021.12.021 10.1016/j.tcs.2021.12.021
Di Wang, Jan Hoffmann, and Thomas Reps. 2021. Central Moment Analysis for Cost Accumulators in Probabilistic Programs. In Proc. of PLDI. https://doi.org/10.1145/3453483.3454062 10.1145/3453483.3454062
Gilles Barthe, Joost-Pieter Katoen, and Alexandra Silva. 2020. Foundations of Probabilistic Programming. Cambridge University Press. https://doi.org/10.1017/9781108770750 10.1017/9781108770750
Marta Z. Kwiatkowska, Gethin Norman, and David Parker. 2012. Probabilistic Verification of Herman’s Self-Stabilisation Algorithm. Formal Aspects of Computing, https://doi.org/10.1007/s00165-012-0227-6 10.1007/s00165-012-0227-6
Christel Baier and Joost-Pieter Katoen. 2008. Principles of model checking. MIT Press. ISBN 978-0-262-02649-9
Enric Rodríguez-carbonell and Deepak Kapur. 2004. Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations. In Proc. of ISSAC. https://doi.org/10.1145/1005285.1005324 10.1145/1005285.1005324
Yijun Feng, Lijun Zhang, David N. Jansen, Naijun Zhan, and Bican Xia. 2017. Finding Polynomial Loop Invariants for Probabilistic Programs. In Proc. of ATVA. https://doi.org/10.1007/978-3-319-68167-2_26 10.1007/978-3-319-68167-2_26
Andreas Humenberger, Maximilian Jaroschek, and Laura Kovács. 2018. Invariant Generation for Multi-Path Loops with Polynomial Assignments. In Proc. of VMCAI. https://doi.org/10.1007/978-3-319-73721-8_11 10.1007/978-3-319-73721-8_11
Ezio Bartocci, Laura Kovács, and Miroslav Stankovic. 2020. Mora - Automatic Generation of Moment-Based Invariants. In Proc. of TACAS. https://doi.org/10.1007/978-3-030-45190-5_28 10.1007/978-3-030-45190-5_28
Jialu Bao, Nitesh Trivedi, Drashti Pathak, Justin Hsu, and Subhajit Roy. 2022. Data-Driven Invariant Learning for Probabilistic Programs. In Proc. of CAV. https://d
e_1_2_1_60_1
e_1_2_1_20_1
e_1_2_1_41_1
e_1_2_1_24_1
e_1_2_1_45_1
e_1_2_1_22_1
e_1_2_1_43_1
e_1_2_1_28_1
e_1_2_1_49_1
e_1_2_1_26_1
e_1_2_1_47_1
e_1_2_1_31_1
e_1_2_1_54_1
e_1_2_1_8_1
e_1_2_1_56_1
e_1_2_1_6_1
e_1_2_1_12_1
e_1_2_1_35_1
e_1_2_1_50_1
e_1_2_1_4_1
e_1_2_1_10_1
e_1_2_1_33_1
e_1_2_1_52_1
e_1_2_1_2_1
e_1_2_1_16_1
e_1_2_1_39_1
e_1_2_1_14_1
e_1_2_1_37_1
e_1_2_1_58_1
e_1_2_1_18_1
e_1_2_1_42_1
e_1_2_1_40_1
e_1_2_1_23_1
e_1_2_1_46_1
e_1_2_1_21_1
e_1_2_1_44_1
e_1_2_1_27_1
e_1_2_1_25_1
e_1_2_1_48_1
e_1_2_1_29_1
Baier Christel (e_1_2_1_1_1)
e_1_2_1_7_1
e_1_2_1_30_1
e_1_2_1_55_1
e_1_2_1_5_1
e_1_2_1_57_1
e_1_2_1_3_1
e_1_2_1_13_1
e_1_2_1_34_1
e_1_2_1_51_1
e_1_2_1_11_1
e_1_2_1_32_1
e_1_2_1_53_1
e_1_2_1_17_1
e_1_2_1_38_1
e_1_2_1_15_1
e_1_2_1_36_1
e_1_2_1_59_1
e_1_2_1_9_1
e_1_2_1_19_1
References_xml – reference: Marta Z. Kwiatkowska, Gethin Norman, and David Parker. 2012. Probabilistic Verification of Herman’s Self-Stabilisation Algorithm. Formal Aspects of Computing, https://doi.org/10.1007/s00165-012-0227-6 10.1007/s00165-012-0227-6
– reference: Zoubin Ghahramani. 2015. Probabilistic Machine Learning and Artificial Intelligence. Nature, https://doi.org/10.1038/nature14541 10.1038/nature14541
– reference: Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady, and Ehsan Kafshdar Goharshady. 2020. Polynomial Invariant Generation for Non-deterministic Recursive Programs. In Proc. of PLDI. https://doi.org/10.1145/3385412 10.1145/3385412
– reference: Zachary Kincaid, John Cyphert, Jason Breck, and T. Reps. 2018. Non-Linear Reasoning for Invariant Synthesis. In Proc. of POPL. https://doi.org/10.1145/3158142 10.1145/3158142
– reference: Annabelle McIver and Carroll Morgan. 2005. Abstraction, Refinement and Proof for Probabilistic Systems. Springer. https://doi.org/10.1007/b138392 10.1007/b138392
– reference: Steven Holtzen, Sebastian Junges, Marcell Vazquez-Chanlatte, Todd D. Millstein, Sanjit A. Seshia, and Guy Van den Broeck. 2021. Model Checking Finite-Horizon Markov Chains with Probabilistic Inference. In Proc. of CAV. https://doi.org/10.1007/978-3-030-81688-9_27 10.1007/978-3-030-81688-9_27
– reference: Gilles Barthe, Joost-Pieter Katoen, and Alexandra Silva. 2020. Foundations of Probabilistic Programming. Cambridge University Press. https://doi.org/10.1017/9781108770750 10.1017/9781108770750
– reference: Stéphane Boucheron, Gábor Lugosi, and Pascal Massart. 2013. Concentration Inequalities - A Nonasymptotic Theory of Independence. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199535255.001.0001 10.1093/acprof:oso/9780199535255.001.0001
– reference: Di Wang, Jan Hoffmann, and Thomas Reps. 2021. Central Moment Analysis for Cost Accumulators in Probabilistic Programs. In Proc. of PLDI. https://doi.org/10.1145/3453483.3454062 10.1145/3453483.3454062
– reference: Yi Chou, Hansol Yoon, and Sriram Sankaranarayanan. 2020. Predictive Runtime Monitoring of Vehicle Models Using Bayesian Estimation and Reachability Analysis. In Proc. of IROS. https://doi.org/10.1109/IROS45743.2020.9340755 10.1109/IROS45743.2020.9340755
– reference: Milton F. Maritz. 2020. A Note on Exact Solutions of the Logistic Map. Chaos: An Interdisciplinary Journal of Nonlinear Science, https://doi.org/10.1063/1.5125097 10.1063/1.5125097
– reference: Marcel Moosbrugger, Miroslav Stankovič, Ezio Bartocci, and Laura Kovács. 2022. This is the Moment for Probabilistic Loops - Artifact (Polar). https://doi.org/10.5281/zenodo.7055030 10.5281/zenodo.7055030
– reference: Timon Gehr, Sasa Misailovic, and Martin T. Vechev. 2016. PSI: Exact Symbolic Inference for Probabilistic Programs. In Proc. of CAV. https://doi.org/10.1007/978-3-319-41528-4_4 10.1007/978-3-319-41528-4_4
– reference: Azadeh Farzan and Zachary Kincaid. 2015. Compositional Recurrence Analysis. In Proc. of FMCAD. https://doi.org/10.1109/FMCAD.2015.7542253 10.1109/FMCAD.2015.7542253
– reference: Håkan L. S. Younes and Reid G. Simmons. 2006. Statistical probabilistic model checking with a focus on time-bounded properties. Inf. Comput., https://doi.org/10.1016/j.ic.2006.05.002 10.1016/j.ic.2006.05.002
– reference: 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 Proc. of SAS. https://doi.org/10.1007/978-3-642-15769-1_24 10.1007/978-3-642-15769-1_24
– reference: Yijun Feng, Lijun Zhang, David N. Jansen, Naijun Zhan, and Bican Xia. 2017. Finding Polynomial Loop Invariants for Probabilistic Programs. In Proc. of ATVA. https://doi.org/10.1007/978-3-319-68167-2_26 10.1007/978-3-319-68167-2_26
– reference: Steven Holtzen, Guy Van den Broeck, and Todd D. Millstein. 2020. Scaling Exact Inference for Discrete Probabilistic Programs. In Proc. of OOPSLA. https://doi.org/10.1145/3428208 10.1145/3428208
– reference: Friedrich Gretz, Joost-Pieter Katoen, and Annabelle McIver. 2013. Prinsys - On a Quest for Probabilistic Loop Invariants. In Proc. of QEST. https://doi.org/10.1007/978-3-642-40196-1_17 10.1007/978-3-642-40196-1_17
– reference: Andreas Humenberger, Maximilian Jaroschek, and Laura Kovács. 2017. Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences. In Proc. of ISSAC. https://doi.org/10.1145/3087604.3087623 10.1145/3087604.3087623
– reference: Steven de Oliveira, Saddek Bensalem, and Virgile Prevosto. 2016. Polynomial Invariants by Linear Algebra. In Proc. of ATVA. https://doi.org/10.1007/978-3-319-46520-3_30 10.1007/978-3-319-46520-3_30
– reference: Jialu Bao, Nitesh Trivedi, Drashti Pathak, Justin Hsu, and Subhajit Roy. 2022. Data-Driven Invariant Learning for Probabilistic Programs. In Proc. of CAV. https://doi.org/10.1007/978-3-031-13185-1_3 10.1007/978-3-031-13185-1_3
– reference: Dominik Gruntz. 1996. On Computing Limits in a Symbolic Manipulation System. Ph. D. Dissertation. ETH Zürich. https://doi.org/10.3929/ETHZ-A-001631582 10.3929/ETHZ-A-001631582
– reference: Robert M. May. 1976. Simple Mathematical Models With Very Complicated Dynamics. Nature, https://doi.org/10.1038/261459a0 10.1038/261459a0
– reference: John E. Kolassa. 2006. Series Approximation Methods in Statistics. Springer. https://doi.org/10.1007/0-387-32227-2 10.1007/0-387-32227-2
– reference: Rajeev Motwani and Prabhakar Raghavan. 1995. Randomized Algorithms. Cambridge University Press. https://doi.org/10.1017/cbo9780511814075 10.1017/cbo9780511814075
– reference: Benjamin Lucien Kaminski, Joost-Pieter Katoen, and Christoph Matheja. 2019. On the Hardness of Analyzing Probabilistic Programs. Acta Informatica, https://doi.org/10.1007/s00236-018-0321-1 10.1007/s00236-018-0321-1
– reference: Wilfred K. Hastings. 1970. Monte Carlo Sampling Methods Using Markov Chains and Their Applications. Biometrika, https://doi.org/10.2307/2334940 10.2307/2334940
– reference: Ezio Bartocci, Laura Kovács, and Miroslav Stankovic. 2020. Analysis of Bayesian Networks via Prob-Solvable Loops. In Proc. of ICTAC. https://doi.org/10.1007/978-3-030-64276-1 10.1007/978-3-030-64276-1
– reference: Christel Baier and Joost-Pieter Katoen. 2008. Principles of model checking. MIT Press. ISBN 978-0-262-02649-9
– reference: Jason Breck, John Cyphert, Zachary Kincaid, and Thomas W. Reps. 2020. Templates and Recurrences: Better Together. In Proc. of PLDI. https://doi.org/10.1145/3385412.3386035 10.1145/3385412.3386035
– reference: Praveena Narayanan, Jacques Carette, Wren Romano, Chung chieh Shan, and Robert Zinkov. 2016. Probabilistic Inference by Program Transformation in Hakaru (System Description). In Proc. of FLOPS. https://doi.org/10.1007/978-3-319-29604-3_5 10.1007/978-3-319-29604-3_5
– reference: Feras A. Saad, Martin C. Rinard, and Vikash K. Mansinghka. 2021. SPPL: Probabilistic Programming With Fast Exact Symbolic Inference. In Proc. of PLDI. https://doi.org/10.1145/3453483.3454078 10.1145/3453483.3454078
– reference: Manuel Kauers and Peter Paule. 2011. The Concrete Tetrahedron - Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates. Springer. https://doi.org/10.1007/978-3-7091-0445-3 10.1007/978-3-7091-0445-3
– reference: Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, and Federico Olmedo. 2016. Weakest Precondition Reasoning for Expected Run-Times of Probabilistic Programs. In Proc. of ESOP. https://doi.org/10.1007/978-3-662-49498-1 10.1007/978-3-662-49498-1
– reference: Dexter Kozen. 1985. A Probabilistic PDL. J. Comput. System Sci., https://doi.org/10.1016/0022-0000(85)90012-1 10.1016/0022-0000(85)90012-1
– reference: Andreas Humenberger, Maximilian Jaroschek, and Laura Kovács. 2018. Invariant Generation for Multi-Path Loops with Polynomial Assignments. In Proc. of VMCAI. https://doi.org/10.1007/978-3-319-73721-8_11 10.1007/978-3-319-73721-8_11
– reference: Miroslav Stankovic, Ezio Bartocci, and Laura Kovács. 2022. Moment-Based Analysis of Bayesian Network Properties. Theor. Comput. Sci., https://doi.org/10.1016/j.tcs.2021.12.021 10.1016/j.tcs.2021.12.021
– reference: Stanley L. Warner. 1965. Randomized Response: A Survey Technique for Eliminating Evasive Answer Bias. J. Am. Stat. Assoc., https://doi.org/10.1080/01621459.1965.10480775 10.1080/01621459.1965.10480775
– reference: Satoshi Kura, Natsuki Urabe, and Ichiro Hasuo. 2019. Tail Probabilities for Randomized Program Runtimes via Martingales for Higher Moments. In Proc. of TACAS. https://doi.org/10.1007/978-3-030-17465-1_8 10.1007/978-3-030-17465-1_8
– reference: Enric Rodríguez-carbonell and Deepak Kapur. 2004. Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations. In Proc. of ISSAC. https://doi.org/10.1145/1005285.1005324 10.1145/1005285.1005324
– reference: 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 Proc. of CAV. https://doi.org/10.1007/978-3-030-81688-9_25 10.1007/978-3-030-81688-9_25
– reference: Zachary Kincaid, Jason Breck, John Cyphert, and T. Reps. 2019. Closed Forms for Numerical Loops. In Proc. of POPL. https://doi.org/10.1145/3290368 10.1145/3290368
– reference: Joost-Pieter Katoen, Ivan S. Zapreev, Ernst Moritz Hahn, Holger Hermanns, and David N. Jansen. 2011. The Ins and Outs of the Probabilistic Model Checker MRMC. Perform. Eval., https://doi.org/10.1016/j.peva.2010.04.001 10.1016/j.peva.2010.04.001
– reference: Guillaume Claret, Sriram K. Rajamani, Aditya V. Nori, Andrew D. Gordon, and Johannes Borgström. 2013. Bayesian Inference Using Data Flow Analysis. In Proc. of ESEC/FSE. https://doi.org/10.1145/2491411.2491423 10.1145/2491411.2491423
– reference: Ezio Bartocci, Laura Kovács, and Miroslav Stankovic. 2019. Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops. In Proc. of ATVA. https://doi.org/10.1007/978-3-030-31784-3_15 10.1007/978-3-030-31784-3_15
– reference: Konstantin Selyunin, Denise Ratasich, Ezio Bartocci, Md. Ariful Islam, Scott A. Smolka, and Radu Grosu. 2015. Neural Programming: Towards Adaptive Control in Cyber-Physical Systems. In Proc. of CDC. https://doi.org/10.1109/CDC.2015.7403319 10.1109/CDC.2015.7403319
– reference: Laura Kovács. 2008. Reasoning Algebraically About P-Solvable Loops. In Proc. of TACAS. https://doi.org/10.1007/978-3-540-78800-3_18 10.1007/978-3-540-78800-3_18
– reference: Olivier Bouissou, Eric Goubault, Sylvie Putot, Aleksandar Chakarov, and Sriram Sankaranarayanan. 2016. Uncertainty Propagation Using Probabilistic Affine Forms and Concentration of Measure Inequalities. In Proc. of TACAS. https://doi.org/10.1007/978-3-662-49674-9_13 10.1007/978-3-662-49674-9_13
– reference: Yu-Fang Chen, Chih-Duo Hong, Bow-Yaw Wang, and Lijun Zhang. 2015. Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation. In Proc. of CAV. https://doi.org/10.1007/978-3-319-21690-4 10.1007/978-3-319-21690-4
– reference: Rick Durrett. 2019. Probability: Theory and Examples. Cambridge University Press. https://doi.org/10.1017/9781108591034 10.1017/9781108591034
– reference: Christian Dehnert, Sebastian Junges, Joost-Pieter Katoen, and Matthias Volk. 2017. A Storm is Coming: A Modern Probabilistic Model Checker. In Proc. of CAV. https://doi.org/10.1007/978-3-319-63390-9 10.1007/978-3-319-63390-9
– reference: Richard M. Karp. 1994. Probabilistic Recurrence Relations. J. ACM, https://doi.org/10.1145/195613.195632 10.1145/195613.195632
– reference: Ezio Bartocci, Laura Kovács, and Miroslav Stankovic. 2020. Mora - Automatic Generation of Moment-Based Invariants. In Proc. of TACAS. https://doi.org/10.1007/978-3-030-45190-5_28 10.1007/978-3-030-45190-5_28
– reference: Aleksandar Chakarov and Sriram Sankaranarayanan. 2014. Expectation Invariants for Probabilistic Program Loops as Fixed Points. In Proc. of SAS. https://doi.org/10.1007/978-3-319-10936-7_6 10.1007/978-3-319-10936-7_6
– reference: Ted Herman. 1990. Probabilistic Self-Stabilization. Inform. Process. Lett., https://doi.org/10.1016/0020-0190(90)90107-9 10.1016/0020-0190(90)90107-9
– reference: Gilles Barthe, Boris Köpf, Federico Olmedo, and Santiago Zanella Béguelin. 2012. Probabilistic Relational Reasoning for Differential Privacy. In Proc. of POPL. https://doi.org/10.1145/2103656.2103670 10.1145/2103656.2103670
– reference: Marta Z. Kwiatkowska, Gethin Norman, and David Parker. 2011. PRISM 4.0: Verification of Probabilistic Real-Time Systems. In Proc. of CAV. https://doi.org/10.1007/978-3-642-22110-1 10.1007/978-3-642-22110-1
– reference: Gilles Barthe, Thomas Espitau, Luis María Ferrer Fioriti, and Justin Hsu. 2016. Synthesizing Probabilistic Invariants via Doob’s Decomposition. In Proc. of CAV. https://doi.org/10.1007/978-3-319-41528-4_3 10.1007/978-3-319-41528-4_3
– reference: Gilles Barthe, Benjamin Grégoire, and Santiago Zanella Béguelin. 2012. Probabilistic Relational Hoare Logics for Computer-Aided Security Proofs. In Proc. of MPC. https://doi.org/10.1007/978-3-642-31113-0 10.1007/978-3-642-31113-0
– ident: e_1_2_1_10_1
  doi: 10.1007/978-3-030-81688-9_25
– ident: e_1_2_1_49_1
  doi: 10.1038/261459a0
– ident: e_1_2_1_19_1
  doi: 10.1007/978-3-319-46520-3_30
– ident: e_1_2_1_39_1
  doi: 10.1007/978-3-7091-0445-3
– ident: e_1_2_1_26_1
  doi: 10.1007/978-3-642-40196-1_17
– ident: e_1_2_1_53_1
  doi: 10.1007/978-3-319-29604-3_5
– ident: e_1_2_1_18_1
  doi: 10.1145/2491411.2491423
– ident: e_1_2_1_30_1
  doi: 10.1145/3428208
– ident: e_1_2_1_14_1
  doi: 10.1007/978-3-319-10936-7_6
– ident: e_1_2_1_27_1
  doi: 10.3929/ETHZ-A-001631582
– ident: e_1_2_1_32_1
  doi: 10.1145/3087604.3087623
– ident: e_1_2_1_42_1
  doi: 10.1007/0-387-32227-2
– ident: e_1_2_1_60_1
  doi: 10.1016/j.ic.2006.05.002
– ident: e_1_2_1_47_1
  doi: 10.1007/s00165-012-0227-6
– ident: e_1_2_1_58_1
  doi: 10.1145/3453483.3454062
– ident: e_1_2_1_45_1
  doi: 10.1007/978-3-030-17465-1_8
– ident: e_1_2_1_2_1
  doi: 10.1007/978-3-031-13185-1_3
– ident: e_1_2_1_41_1
  doi: 10.1145/3158142
– ident: e_1_2_1_40_1
  doi: 10.1145/3290368
– ident: e_1_2_1_38_1
  doi: 10.1016/j.peva.2010.04.001
– volume-title: Principles of model checking
  ident: e_1_2_1_1_1
– ident: e_1_2_1_13_1
  doi: 10.1145/3385412.3386035
– ident: e_1_2_1_36_1
  doi: 10.1145/195613.195632
– ident: e_1_2_1_48_1
  doi: 10.1063/1.5125097
– ident: e_1_2_1_31_1
  doi: 10.1007/978-3-030-81688-9_27
– ident: e_1_2_1_15_1
  doi: 10.1145/3385412
– ident: e_1_2_1_12_1
  doi: 10.1007/978-3-662-49674-9_13
– ident: e_1_2_1_35_1
  doi: 10.1007/978-3-662-49498-1
– ident: e_1_2_1_54_1
  doi: 10.1145/1005285.1005324
– ident: e_1_2_1_6_1
  doi: 10.1145/2103656.2103670
– ident: e_1_2_1_43_1
  doi: 10.1007/978-3-540-78800-3_18
– ident: e_1_2_1_3_1
  doi: 10.1007/978-3-319-41528-4_3
– ident: e_1_2_1_20_1
  doi: 10.1007/978-3-319-63390-9
– ident: e_1_2_1_24_1
  doi: 10.1007/978-3-319-41528-4_4
– ident: e_1_2_1_25_1
  doi: 10.1038/nature14541
– ident: e_1_2_1_8_1
  doi: 10.1007/978-3-030-64276-1
– ident: e_1_2_1_22_1
  doi: 10.1109/FMCAD.2015.7542253
– ident: e_1_2_1_23_1
  doi: 10.1007/978-3-319-68167-2_26
– ident: e_1_2_1_37_1
  doi: 10.1007/978-3-642-15769-1_24
– ident: e_1_2_1_5_1
  doi: 10.1017/9781108770750
– ident: e_1_2_1_55_1
  doi: 10.1145/3453483.3454078
– ident: e_1_2_1_57_1
  doi: 10.1016/j.tcs.2021.12.021
– ident: e_1_2_1_50_1
  doi: 10.1007/b138392
– ident: e_1_2_1_44_1
  doi: 10.1016/0022-0000(85)90012-1
– ident: e_1_2_1_46_1
  doi: 10.1007/978-3-642-22110-1
– ident: e_1_2_1_17_1
  doi: 10.1109/IROS45743.2020.9340755
– ident: e_1_2_1_56_1
  doi: 10.1109/CDC.2015.7403319
– ident: e_1_2_1_16_1
  doi: 10.1007/978-3-319-21690-4
– ident: e_1_2_1_11_1
  doi: 10.1093/acprof:oso/9780199535255.001.0001
– ident: e_1_2_1_29_1
  doi: 10.1016/0020-0190(90)90107-9
– ident: e_1_2_1_52_1
  doi: 10.1017/cbo9780511814075
– ident: e_1_2_1_33_1
  doi: 10.1007/978-3-319-73721-8_11
– ident: e_1_2_1_21_1
  doi: 10.1017/9781108591034
– ident: e_1_2_1_59_1
  doi: 10.1080/01621459.1965.10480775
– ident: e_1_2_1_7_1
  doi: 10.1007/978-3-030-31784-3_15
– ident: e_1_2_1_28_1
  doi: 10.2307/2334940
– ident: e_1_2_1_34_1
  doi: 10.1007/s00236-018-0321-1
– ident: e_1_2_1_4_1
  doi: 10.1007/978-3-642-31113-0
– ident: e_1_2_1_9_1
  doi: 10.1007/978-3-030-45190-5_28
– ident: e_1_2_1_51_1
  doi: 10.5281/zenodo.7055030
SSID ssj0001934839
Score 2.4070253
Snippet We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially...
SourceID crossref
acm
SourceType Enrichment Source
Index Database
Publisher
StartPage 1497
SubjectTerms Computing methodologies
Markov processes
Mathematics of computing
Random walks and Markov chains
Symbolic and algebraic algorithms
Theory of computation
SubjectTermsDisplay Computing methodologies -- Symbolic and algebraic algorithms
Mathematics of computing -- Markov processes
Theory of computation -- Random walks and Markov chains
Title This is the moment for probabilistic loops
URI https://dl.acm.org/doi/10.1145/3563341
Volume 6
WOSCitedRecordID wos001083750200055&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 2475-1421
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0001934839
  issn: 2475-1421
  databaseCode: M~E
  dateStart: 20170101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Nb9QwELWgcOBCoYAoLSgHxAEUkQ_Hjo-rtohDt12Jgnpb2Y5drbqbrDbbVcWB386M7WRD1QMckKIoSkbeTZ41nhm_mSHkPawpVZawKqZM25gKmcel5SZONStUYniVu2YwP0752Vl5eSkmgavaunYCvK7L21ux_K9Qwz0AG1Nn_wHuflC4AdcAOpwBdjj_JfCzFtuUo0W5aNxeP1IJsXOMq6aLhZk_zZtm2Q4N00m_kDlux-hojNsIgb21wHhCF9nsjfBx07RqdXN15VEfY9Zkz9fA7sTXzWbmjNVjT9CHBXkuN9vY6WrdaO3YBCc_PR3MJ-Fs3O596hlMmLgth7EJcGu3St3PpsB3d_oso7yIU-oTojvlywZz7Px88u10lA3UKbhvfLA0Y6-m-9U-xQoZecHy3JfRulNDOzx5SB5lvBCov8e_BqE4kVOwE31KNY71OcijxaIXA4tlYHpcPCNPg88QjTzWz8kDU--R3a4fRxTU8wvyEaGP4ADoIw99BNBHf0AfOehfku9fTi6OvsahF0YsM87XyKKxsqTW8EwKSbm03ML_TkyKPiUrFTxRhinBrVWZ1kyAK6xA21apLqrc5K_ITt3U5jWJNGe2MjYpRSYpvGUJ4ipV3CZMSMbkPtmDt54ufbWTafgW--RD9xWmOpSPxy4m86lPbS-2glEv2I1xR-TNvb9wQJ5s59Ah2Vmvbsxb8lhv1rN29c5B9huAE1lM
linkProvider ISSN International Centre
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=This+is+the+moment+for+probabilistic+loops&rft.jtitle=Proceedings+of+ACM+on+programming+languages&rft.au=Moosbrugger%2C+Marcel&rft.au=Stankovi%C4%8D%2C+Miroslav&rft.au=Bartocci%2C+Ezio&rft.au=Kov%C3%A1cs%2C+Laura&rft.date=2022-10-31&rft.pub=ACM&rft.eissn=2475-1421&rft.volume=6&rft.issue=OOPSLA2&rft.spage=1497&rft.epage=1525&rft_id=info:doi/10.1145%2F3563341&rft.externalDocID=3563341
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2475-1421&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2475-1421&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2475-1421&client=summon