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Abstract This work is devoted to formal reasoning on relational properties of probabilistic imperative programs. Relational properties are properties which relate the execution of two programs (possibly the same one) on two initial memories. We aim at extending the algebraic approach of Kleene Algebras with Tests (KAT) to relational properties of probabilistic programs. For that we consider the approach of Guarded Kleene Algebras with Tests (GKAT), which can be used for representing probabilistic programs, and define a relational version of it, called Bi-guarded Kleene Algebras with Tests (BiGKAT) together with a semantics. We show that the setting of BiGKAT is expressive enough to encode a finitary version of probabilistic Relational Hoare Logic (pRHL) (without the While rule), a program logic that has been introduced in the literature for the verification of relational properties of probabilistic programs. We also discuss the additional expressivity brought by BiGKAT.
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An Algebra of Alignment for Relational Verification
Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational invariants and relational procedure specs, which in turn enables automation and modular reasoning. Alignment has been explored in terms of trace pairs, deductive rules of relational Hoare logics (RHL), and several forms of product automata. This article shows how a simple extension of Kleene Algebra with Tests (KAT), called BiKAT, subsumes prior formulations, including alignment witnesses for forall-exists properties, which brings to light new RHL-style rules for such properties. Alignments can be discovered algorithmically or devised manually but, in either case, their adequacy with respect to the original programs must be proved; an explicit algebra enables constructive proof by equational reasoning. Furthermore our approach inherits algorithmic benefits from existing KAT-based techniques and tools, which are applicable to a range of semantic models.
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- PAR ID:
- 10427308
- Publisher / Repository:
- ACM Journals
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 7
- Issue:
- POPL
- ISSN:
- 2475-1421
- Page Range / eLocation ID:
- 573 to 603
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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