# On incorrectness logic and Kleene algebra with top and tests

@article{Zhang2021OnIL, title={On incorrectness logic and Kleene algebra with top and tests}, author={Cheng Zhang and Arthur Azevedo de Amorim and Marco Gaboardi}, journal={Proceedings of the ACM on Programming Languages}, year={2021}, volume={6}, pages={1 - 30} }

Kleene algebra with tests (KAT) is a foundational equational framework for reasoning about programs, which has found applications in program transformations, networking and compiler optimizations, among many other areas. In his seminal work, Kozen proved that KAT subsumes propositional Hoare logic, showing that one can reason about the (partial) correctness of while programs by means of the equational theory of KAT. In this work, we investigate the support that KAT provides for reasoning about…

## 6 Citations

### Local Completeness Logic on Kleene Algebra with Tests

- Computer ScienceSAS
- 2022

It is generalized by studying how KATs extended either with a modal diamond operator or with a top element are able to represent the local completeness logic LCL, to show that the LCL proof system is logically sound and, under some hypotheses, complete.

### An Algebra of Alignment for Relational Verification

- Computer ScienceProceedings of the ACM on Programming Languages
- 2023

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.

### Four Rules for Converting Complex Loops to Regular Expressions

- Computer Science2022 9th International Conference on Dependable Systems and Their Applications (DSA)
- 2022

The paper presents a new method for constructing regress expressions for complex loops and introduces four types of loops and gives rules for converting these loops to regular expressions.

### Completeness Theorems for Kleene Algebra with Top

- MathematicsCONCUR
- 2022

Two completeness results for Kleene algebra with a top element are proved, with respect to languages and binary relations, which are relative to any axiomatisation of the algebra of regular events.

### On Tools for Completeness of Kleene Algebra with Hypotheses

- MathematicsRAMiCS
- 2021

. In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure speciﬁed by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene…

### On Algebra of Program Correctness and Incorrectness

- Computer ScienceRAMiCS
- 2021

A Kleene algebra with diamond operators and countable joins of tests is used, which embeds IL, and which also is complete for reasoning about the image of the embedding, which unifies correctness and incorrectness reasoning in one formalism.

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A Kleene algebra with diamond operators and countable joins of tests is used, which embeds IL, and which also is complete for reasoning about the image of the embedding, which unifies correctness and incorrectness reasoning in one formalism.

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