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This is the moment for probabilistic loops

https://doi.org/10.1145/3563341
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/0-387-32227-2openalex-snapshot
Series Approximation Methods in Statistics
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Tail Probabilities for Randomized Program Runtimes via Martingales for Higher Moments
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Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops
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Mora - Automatic Generation of Moment-Based Invariants
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Theoretical Aspects of Computing – ICTAC 2020
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Latticed k-Induction with an Application to Probabilistic Programs
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Model Checking Finite-Horizon Markov Chains with Probabilistic Inference
inferredcites →https://doi.org/10.1007/978-3-031-13185-1_3openalex-snapshot
Data-Driven Invariant Learning for Probabilistic Programs
inferredcites →https://doi.org/10.1007/978-3-319-10936-7_6openalex-snapshot
Expectation Invariants for Probabilistic Program Loops as Fixed Points
inferredcites →https://doi.org/10.1007/978-3-319-21690-4openalex-snapshot
Computer Aided Verification
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Probabilistic Inference by Program Transformation in Hakaru (System Description)
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Synthesizing Probabilistic Invariants via Doob’s Decomposition
inferredcites →https://doi.org/10.1007/978-3-319-41528-4_4openalex-snapshot
PSI: Exact Symbolic Inference for Probabilistic Programs
inferredcites →https://doi.org/10.1007/978-3-319-46520-3_30openalex-snapshot
Polynomial Invariants by Linear Algebra
inferredcites →https://doi.org/10.1007/978-3-319-63390-9openalex-snapshot
Computer Aided Verification
inferredcites →https://doi.org/10.1007/978-3-319-68167-2_26openalex-snapshot
Finding Polynomial Loop Invariants for Probabilistic Programs
inferredcites →https://doi.org/10.1007/978-3-319-73721-8_11openalex-snapshot
Invariant Generation for Multi-Path Loops with Polynomial Assignments
inferredcites →https://doi.org/10.1007/978-3-540-78800-3_18openalex-snapshot
Reasoning Algebraically About P-Solvable Loops
inferredcites →https://doi.org/10.1007/978-3-642-15769-1_24openalex-snapshot
Linear-Invariant Generation for Probabilistic Programs:
inferredcites →https://doi.org/10.1007/978-3-642-22110-1openalex-snapshot
Computer aided verification : 23rd international conference, CAV 2011, Snowbird, UT, USA, July 14-20, 2011 : proceedings
inferredcites →https://doi.org/10.1007/978-3-642-31113-0openalex-snapshot
Mathematics of program construction : 11th international conference, MPC 2012, Madrid, Spain, June 25-27, 2012, proceedings
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Prinsys—On a Quest for Probabilistic Loop Invariants
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Programming Languages and Systems
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Uncertainty Propagation Using Probabilistic Affine Forms and Concentration of Measure Inequalities
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The Concrete Tetrahedron
inferredcites →https://doi.org/10.1007/b138392openalex-snapshot
Abstraction, Refinement and Proof for Probabilistic Systems
inferredcites →https://doi.org/10.1007/s00165-012-0227-6openalex-snapshot
Probabilistic verification of Herman’s self-stabilisation algorithm
inferredcites →https://doi.org/10.1007/s00236-018-0321-1openalex-snapshot
On the hardness of analyzing probabilistic programs
inferredcites →https://doi.org/10.1016/0020-0190(90)90107-9openalex-snapshot
Probabilistic self-stabilization
inferredcites →https://doi.org/10.1016/0022-0000(85)90012-1openalex-snapshot
A probabilistic PDL
inferredcites →https://doi.org/10.1016/j.ic.2006.05.002openalex-snapshot
Statistical probabilistic model checking with a focus on time-bounded properties
inferredcites →https://doi.org/10.1016/j.peva.2010.04.001openalex-snapshot
The ins and outs of the probabilistic model checker MRMC
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Moment-based analysis of Bayesian network properties
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Probability
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Foundations of Probabilistic Programming
inferredcites →https://doi.org/10.1017/cbo9780511814075openalex-snapshot
Randomized Algorithms
inferredcites →https://doi.org/10.1038/261459a0openalex-snapshot
Simple mathematical models with very complicated dynamics
inferredcites →https://doi.org/10.1038/nature14541openalex-snapshot
Probabilistic machine learning and artificial intelligence
inferredcites →https://doi.org/10.1063/1.5125097openalex-snapshot
A note on exact solutions of the logistic map
inferredcites →https://doi.org/10.1080/01621459.1965.10480775openalex-snapshot
Randomized Response: A Survey Technique for Eliminating Evasive Answer Bias
inferredcites →https://doi.org/10.1093/acprof:oso/9780199535255.001.0001openalex-snapshot
Concentration Inequalities
inferredcites →https://doi.org/10.1109/cdc.2015.7403319openalex-snapshot
Neural Programming: Towards adaptive control in Cyber-Physical Systems
inferredcites →https://doi.org/10.1109/fmcad.2015.7542253openalex-snapshot
Compositional recurrence analysis
inferredcites →https://doi.org/10.1109/iros45743.2020.9340755openalex-snapshot
Predictive Runtime Monitoring of Vehicle Models Using Bayesian Estimation and Reachability Analysis
inferredcites →https://doi.org/10.1145/1005285.1005324openalex-snapshot
Automatic Generation of Polynomial Loop Invariants
inferredcites →https://doi.org/10.1145/195613.195632openalex-snapshot
Probabilistic recurrence relations
inferredcites →https://doi.org/10.1145/2103656.2103670openalex-snapshot
Probabilistic relational reasoning for differential privacy
inferredcites →https://doi.org/10.1145/2491411.2491423openalex-snapshot
Bayesian inference using data flow analysis
inferredcites →https://doi.org/10.1145/3087604.3087623openalex-snapshot
Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences
inferredcites →https://doi.org/10.1145/3158142openalex-snapshot
Non-linear reasoning for invariant synthesis
inferredcites →https://doi.org/10.1145/3290368openalex-snapshot
Closed forms for numerical loops
inferredcites →https://doi.org/10.1145/3385412openalex-snapshot
Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation
inferredcites →https://doi.org/10.1145/3385412.3386035openalex-snapshot
Templates and recurrences: better together
inferredcites →https://doi.org/10.1145/3428208openalex-snapshot
Scaling exact inference for discrete probabilistic programs
inferredcites →https://doi.org/10.1145/3453483.3454062openalex-snapshot
Central moment analysis for cost accumulators in probabilistic programs
inferredcites →https://doi.org/10.1145/3453483.3454078openalex-snapshot
SPPL: probabilistic programming with fast exact symbolic inference
inferredcites →https://doi.org/10.2307/2334940openalex-snapshot
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
inferredcites →https://doi.org/10.3929/ethz-a-001631582openalex-snapshot
On computing limits in a symbolic manipulation system
inferredcites →https://doi.org/10.5281/zenodo.6807520openalex-snapshot
This is the Moment for Probabilistic Loops - Artifact (Polar)

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/978-3-031-16336-4_1openalex-snapshot
Moment-Based Invariants for Probabilistic Loops with Non-polynomial Assignments
inferred← citeshttps://doi.org/10.1007/978-3-031-27481-7_1openalex-snapshot
Symbolic Computation in Automated Program Reasoning
inferred← citeshttps://doi.org/10.1007/978-3-031-47705-8_2openalex-snapshot
Automated Sensitivity Analysis for Probabilistic Loops
inferred← citeshttps://doi.org/10.1007/978-3-031-68416-6_14openalex-snapshot
Probabilistic Loop Synthesis from Sequences of Moments
inferred← citeshttps://doi.org/10.1007/978-3-031-72621-7_1openalex-snapshot
Quantifying Uncertainty in Probabilistic Loops Without Sampling: A Fully Automated Approach
inferred← citeshttps://doi.org/10.1007/978-3-031-73709-1_10openalex-snapshot
The ProbInG Project: Advancing Automatic Analysis of Probabilistic Loops
inferred← citeshttps://doi.org/10.1007/978-3-031-73709-1_11openalex-snapshot
Towards a Probabilistic Programming Approach to Analyse Collective Adaptive Systems
inferred← citeshttps://doi.org/10.1007/978-3-031-75783-9_10openalex-snapshot
A Unified Framework for Quantitative Analysis of Probabilistic Programs
inferred← citeshttps://doi.org/10.1007/978-3-031-75783-9_8openalex-snapshot
Polar: An Algebraic Analyzer for (Probabilistic) Loops
inferred← citeshttps://doi.org/10.1007/978-3-031-98679-6_1openalex-snapshot
Quantitative Supermartingale Certificates
inferred← citeshttps://doi.org/10.1007/978-3-032-05792-1_15openalex-snapshot
Positive Almost-Sure Termination of Polynomial Random Walks
inferred← citeshttps://doi.org/10.1007/978-3-032-16855-9_5openalex-snapshot
Fixed-Point Reasoning for Stochastic Systems
inferred← citeshttps://doi.org/10.1007/978-3-032-22723-2_8openalex-snapshot
Error Localization, Certificates, and Hints for Probabilistic Program Verification via Slicing
inferred← citeshttps://doi.org/10.1007/978-3-032-26204-2_29openalex-snapshot
Highly Incremental: A Simple Programmatic Approach for Many Objectives
inferred← citeshttps://doi.org/10.1007/978-3-032-26220-2_4openalex-snapshot
Exact Moment Estimation of Stochastic Differential Dynamics
inferred← citeshttps://doi.org/10.1007/978-3-032-32537-2_27openalex-snapshot
Caesar: A Deductive Verifier for Probabilistic Programs
inferred← citeshttps://doi.org/10.1007/s10703-024-00455-0openalex-snapshot
(Un)Solvable loop analysis
inferred← citeshttps://doi.org/10.1016/j.jsc.2025.102551openalex-snapshot
Algebraic and algorithmic methods for computing polynomial loop invariants
inferred← citeshttps://doi.org/10.1145/3586050openalex-snapshot
Exact Recursive Probabilistic Programming
inferred← citeshttps://doi.org/10.1145/3597066.3597150openalex-snapshot
Algebra-Based Loop Analysis
inferred← citeshttps://doi.org/10.1145/3632872openalex-snapshot
Strong Invariants Are Hard: On the Hardness of Strongest Polynomial Invariants for (Probabilistic) Programs
inferred← citeshttps://doi.org/10.1145/3632905openalex-snapshot
Inference of Probabilistic Programs with Moment-Matching Gaussian Mixtures
inferred← citeshttps://doi.org/10.1145/3641545openalex-snapshot
Exact and Approximate Moment Derivation for Probabilistic Loops With Non-Polynomial Assignments
inferred← citeshttps://doi.org/10.1145/3649822openalex-snapshot
Newtonian Program Analysis of Probabilistic Programs
inferred← citeshttps://doi.org/10.1145/3649844openalex-snapshot
Exact Bayesian Inference for Loopy Probabilistic Programs using Generating Functions
inferred← citeshttps://doi.org/10.1145/3666000.3669710openalex-snapshot
Algebraic Tools for Computing Polynomial Loop Invariants
inferred← citeshttps://doi.org/10.1145/3704874openalex-snapshot
Guaranteed Bounds on Posterior Distributions of Discrete Probabilistic Programs with Loops
inferred← citeshttps://doi.org/10.1145/3704894openalex-snapshot
Bluebell: An Alliance of Relational Lifting and Independence for Probabilistic Reasoning
inferred← citeshttps://doi.org/10.1145/3720429openalex-snapshot
Foundations for Deductive Verification of Continuous Probabilistic Programs: From Lebesgue to Riemann and Back
inferred← citeshttps://doi.org/10.1145/3728648openalex-snapshot
Moment-based Density Elicitation with Applications in Probabilistic Loops
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