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Reasoning about Recursive Probabilistic Programs
TL;DR: A wp–style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs and bounds on the expected runtime of recursive programs that can be used to determine the time until termination of such programs are given.
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Abstract: This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the soundness of our wp-calculus with respect to a probabilistic pushdown automaton semantics. We also give a wp-style calculus for obtaining bounds on the expected runtime of recursive programs that can be used to determine the (possibly infinite) time until termination of such programs.
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Citations
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Bounded Expectations: Resource Analysis for Probabilistic Programs
TL;DR: In this paper, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning based on weakest preconditions is presented.
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•Posted Content
Raising Expectations: Automating Expected Cost Analysis with Types.
TL;DR: This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs that is naturally compositional, parametric in the cost model, and supports higher-order functions and inductive data types.
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Quantitative Separation Logic - A Logic for Reasoning about Probabilistic Programs
TL;DR: In this article, the connectives of separation logic, separating conjunction and separating implication, are lifted from predicates to quantities, and a weakest precondition calculus for quantitative reasoning about probabilistic pointer programs in quantitative separation logic is presented.
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A Denotational Semantics for Low-Level Probabilistic Programs with Nondeterminism
Di Wang,Jan Hoffmann,Thomas Reps +2 more
TL;DR: A new formalization of nondeterminism based on powerdomains over sub-probability kernels over control-flow hyper-graphs is developed, which follows an algebraic approach and can be instantiated in different ways as long as certain algebraic properties hold.
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Time-bounded termination analysis for probabilistic programs with delays
Ming Xu,Yuxin Deng +1 more
TL;DR: The goal is to measure those individual execution paths of a PPD that terminates within a given time bound, and to compute the minimum termination probability, i.e. the termination probability under a demonic scheduler that resolves the nondeterminism inherited from probabilistic programs.
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Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Michael Mitzenmacher,Eli Upfal +1 more
- 01 Jan 2005
TL;DR: Preface 1. Events and probability 2. Discrete random variables and expectation 3. Moments and deviations 4. Chernoff bounds 5. Balls, bins and random graphs 6. Probabilistic method 7. Markov chains and random walks 8. Continuous distributions and the Poisson process
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Probabilistic programming
Andrew D. Gordon,Thomas A. Henzinger,Aditya V. Nori,Sriram K. Rajamani +3 more
- 31 May 2014
TL;DR: This paper describes connections this research area called ``Probabilistic Programming" has with programming languages and software engineering, and this includes language design, and the static and dynamic analysis of programs.
Semantics of probabilistic programs
TL;DR: Two complementary but equivalent semantic interpretations of a high level probabilistic programming language are given and how the ordered domains of Scott and others are embedded naturally into these spaces.
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Probabilistic Termination: Soundness, Completeness, and Compositionality
Luis María Ferrer Fioriti,Holger Hermanns +1 more
- 14 Jan 2015
TL;DR: A framework to prove almost sure termination for probabilistic programs with real valued variables, based on ranking supermartingales, which is proven sound and complete for a meaningful class of programs involving randomization and bounded nondeterminism.
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