A Bunched Logic for Conditional Independence

Bao, Jialu; Docherty, Simon; Hsu, Justin; Silva, Alexandra

doi:10.1109/lics52264.2021.9470712

Cited by 9 publications

(4 citation statements)

References 37 publications

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“…Future work includes considering richer classes of QSL and applications of entailment checking such as k-induction [6]. Another interesting direction is the applicability of our reduction to other approaches that aim for local reasoning about the resources employed by probabilistic programs, such as [50,3,5].…”

Section: Discussionmentioning

confidence: 99%

Foundations for Entailment Checking in Quantitative Separation Logic (extended version)

Batz¹,

Fesefeldt²,

Jansen³

et al. 2022

Preprint

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Quantitative separation logic (QSL) is an extension of separation logic (SL) for the verification of probabilistic pointer programs. In QSL, formulae evaluate to real numbers instead of truth values, e.g., the probability of memory-safe termination in a given symbolic heap. As with SL, one of the key problems when reasoning with QSL is entailment: does a formula f entail another formula g? We give a generic reduction from entailment checking in QSL to entailment checking in SL. This allows to leverage the large body of SL research for the automated verification of probabilistic pointer programs. We analyze the complexity of our approach and demonstrate its applicability. In particular, we obtain the first decidability results for the verification of such programs by applying our reduction to a quantitative extension of the well-known symbolic-heap fragment of separation logic.

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Section: Discussionmentioning

confidence: 99%

Foundations for Entailment Checking in Quantitative Separation Logic (extended version)

Batz¹,

Fesefeldt²,

Jansen³

et al. 2022

Preprint

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“…The theoretical aim of our paper is similar to that of Barthe et al [2019], who discuss a separation logic for reasoning about independence, and the follow-up work of Bao et al [2021], who extend the logic to capture conditional independence. One advantage of our method is that the verification of conditional independence is automated by type inference, while it would rely on manual reasoning in the works of Barthe et al [2019] and Bao et al [2021]. On the other hand, the logic approach can be applied to a wider variety of verification tasks.…”

Section: Related Workmentioning

confidence: 97%

Probabilistic programming with densities in SlicStan: efficient, flexible, and deterministic

Gorinova

Gordon

Sutton

2019

Proc. ACM Program. Lang.

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Stan is a probabilistic programming language that has been increasingly used for real-world scalable projects. However, to make practical inference possible, the language sacrifices some of its usability by adopting a block syntax, which lacks compositionality and flexible user-defined functions. Moreover, the semantics of the language has been mainly given in terms of intuition about implementation, and has not been formalised.This paper provides a formal treatment of the Stan language, and introduces the probabilistic programming language SlicStan -a compositional, self-optimising version of Stan. Our main contributions are (1) the formalisation of a core subset of Stan through an operational density-based semantics; (2) the design and semantics of the Stan-like language SlicStan, which facilities better code reuse and abstraction through its compositional syntax, more flexible functions, and information-flow type system; and (3) a formal, semanticpreserving procedure for translating SlicStan to Stan.

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“…LINA is an extension of PSL [Barthe et al 2020], a separation logic for probabilistic independence. Bao et al [2021] propose DIBI, an extension of BI with a non-commutative conjunction, and developed a program logic with DIBI assertions that is capable of proving conditional independence. Batz et al [2019] propose QSL, a separation logic where assertions have a quantitative interpretation, and used their logic to verify probabilistic and heap-manipulating programs.…”

Section: Related Workmentioning

confidence: 99%

A separation logic for negative dependence

Bao

Gaboardi

Hsu

et al. 2022

Proc. ACM Program. Lang.

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Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller (like the number of elements hashed into the other buckets). This is an example of negative dependence , a generalization of probabilistic independence that has recently found interesting applications in algorithm design and machine learning. Despite the usefulness of negative dependence for the analyses of probabilistic data structures, existing verification methods cannot establish this property for randomized programs. To fill this gap, we design LINA, a probabilistic separation logic for reasoning about negative dependence. Following recent works on probabilistic separation logic using separating conjunction to reason about the probabilistic independence of random variables, we use separating conjunction to reason about negative dependence. Our assertion logic features two separating conjunctions, one for independence and one for negative dependence. We generalize the logic of bunched implications (BI) to support multiple separating conjunctions, and provide a sound and complete proof system. Notably, the semantics for separating conjunction relies on a non-deterministic , rather than partial, operation for combining resources. By drawing on closure properties for negative dependence, our program logic supports a Frame-like rule for negative dependence and monotone operations. We demonstrate how LINA can verify probabilistic properties of hash-based data structures and balls-into-bins processes.

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A Bunched Logic for Conditional Independence

Cited by 9 publications

References 37 publications

Foundations for Entailment Checking in Quantitative Separation Logic (extended version)

Foundations for Entailment Checking in Quantitative Separation Logic (extended version)

Probabilistic programming with densities in SlicStan: efficient, flexible, and deterministic

A separation logic for negative dependence

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