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A completeness theorem for Kleene algebras and the algebra of regular events
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Theoretical Computer Science
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ACM Transactions on Programming Languages and Systems (TOPLAS)
Refinement and demonic semantics
Relational methods in computer science
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Refinement algebra with operators for enabledness and termination
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Latest news about demonic algebra with domain
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
On the structure of demonic refinement algebras with enabledness and termination
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Partial, total and general correctness
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Unifying recursion in partial, total and general correctness
UTP'10 Proceedings of the Third international conference on Unifying theories of programming
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Omega algebra, demonic refinement algebra and commands
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Unifying correctness statements
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
Extended designs algebraically
Science of Computer Programming
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We first recall the concept of Kleene algebra with domain (KAD). Then we explain how to use the operators of KAD to define a demonic refinement ordering and demonic operators (many of these definitions come from the literature). Then, taking the properties of the KAD-based demonic operators as a guideline, we axiomatise an algebra that we call Demonic algebra with domain (DAD). The laws of DAD not concerning the domain operator agree with those given in the 1987 CACM paper Laws of programming by Hoare et al. Finally, we investigate the relationship between demonic algebras with domain and KAD-based demonic algebras. The question is whether every DAD is isomorphic to a KAD-based demonic algebra. We show that it is not the case in general. However, if a DAD $\mathcal{D}$ is isomorphic to a demonic algebra based on a KAD $\mathcal{K}$, then it is possible to construct a KAD isomorphic to $\mathcal{K}$ using the operators of $\mathcal{D}$. We also describe a few open problems.