article

Kleene algebra with domain

Authors:

Jules Desharnais,

Bernhard Möller,

Georg StruthAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 7, Issue 4

Pages 798 - 833

https://doi.org/10.1145/1183278.1183285

Published: 01 October 2006 Publication History

Abstract

We propose Kleene algebra with domain (KAD), an extension of Kleene algebra by simple equational axioms for a domain and a codomain operation. KAD considerably augments the expressiveness of Kleene algebra, in particular for the specification and analysis of programs and state transition systems. We develop the basic calculus, present the most interesting models and discuss some related theories. We demonstrate applicability by two examples: algebraic reconstructions of Noethericity and propositional Hoare logic based on equational reasoning.

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 7, Issue 4

October 2006

226 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/1183278

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Copyright © 2006 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 2006

Published in TOCL Volume 7, Issue 4

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Cited By

ten Cate BKappé T(2025)Algebras for Deterministic Computation Are Inherently IncompleteProceedings of the ACM on Programming Languages10.1145/37048619:POPL(718-744)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704861
Sedlár I(2024)Implicational Kleene algebra with domain and the substructural logic of partial correctnessMathematical Structures in Computer Science10.1017/S0960129524000045(1-16)Online publication date: 4-Mar-2024
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Nakamura Y(2024)Undecidability of the Positive Calculus of Relations with Transitive Closure and Difference: Hypothesis Elimination Using Graph LoopsRelational and Algebraic Methods in Computer Science10.1007/978-3-031-68279-7_13(207-224)Online publication date: 19-Aug-2024
https://dl.acm.org/doi/10.1007/978-3-031-68279-7_13
Arshad HPicazo-Sanchez PJohansen CSchneider G(2023)Attribute-based encryption with enforceable obligationsJournal of Cryptographic Engineering10.1007/s13389-023-00317-113:3(343-371)Online publication date: 29-Apr-2023
https://doi.org/10.1007/s13389-023-00317-1
Fahrenberg UJohansen CStruth GZiemiański K(2023)Catoids and modal convolution algebrasAlgebra universalis10.1007/s00012-023-00805-984:2Online publication date: 25-Feb-2023
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Fahrenberg UJohansen CStruth GZiemiański K(2022)Domain Semirings UnitedActa Cybernetica10.14232/actacyb.291111Online publication date: 5-Jan-2022
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