A generalization of Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Operational semantics and generalized weakest preconditions
Science of Computer Programming - Special issue on mathematics of program construction
Information Processing Letters - Special issue on the calculational method
Information Processing Letters - Special issue on the calculational method
ACM Transactions on Programming Languages and Systems (TOPLAS)
Handbook of formal languages, vol. 3
Computation calculus bridging a formalization gap
Science of Computer Programming - Special issue on mathematics of program construction
A generalized control structure and its formal definition
Communications of the ACM
Refinement Calculus: A Systematic Introduction
Refinement Calculus: A Systematic Introduction
Proceedings of the ESPRIT Working Group 8533 on Prospects for Hardware Foundations: NADA - New Hardware Design Methods, Survey Chapters
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
An Operational Semantics for the Guarded Command Language
Proceedings of the Second International Conference on Mathematics of Program Construction
Computation Calculus - Bridging a Formalization Gap
MPC '98 Proceedings of the Mathematics of Program Construction
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
From Kleene Algebra to Refinement Algebra
MPC '02 Proceedings of the 6th International Conference on Mathematics of Program Construction
A Complete Axiomatization of Interval Temporal Logic with Infinite Time
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
ACM Transactions on Computational Logic (TOCL)
Towards an algebra of hybrid systems
RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
UTP'06 Proceedings of the First international conference on Unifying Theories of Programming
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
Refinement algebra with operators for enabledness and termination
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Domain Axioms for a Family of Near-Semirings
AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
Enabledness and termination in refinement algebra
Science of Computer Programming
A sketch of a dynamic epistemic semiring
Information and Computation
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
Automated reasoning for hybrid systems: two case studies
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
Non-termination in idempotent semirings
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
Unifying recursion in partial, total and general correctness
UTP'10 Proceedings of the Third international conference on Unifying theories of programming
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Lazy semiring neighbours and some applications
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
Reverse exchange for concurrency and local reasoning
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
Unifying correctness statements
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
Unifying lazy and strict computations
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Extended designs algebraically
Science of Computer Programming
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We propose a relaxation of Kleene algebra by giving up strictness and right-distributivity of composition. This allows the subsumption of Dijkstra's computation calculus, Cohen's omega algebra and von Wright's demonic refinement algebra. Moreover, by adding domain and codomain operators we can also incorporate modal operators. We show that predicate transformers form lazy Kleene algebras, the disjunctive and conjunctive ones even lazy omega Kleene algebras. We also briefly sketch two further applications: a modal lazy Kleene algebra of commands modelling total correctness and another one that abstractly characterizes sets of trajectories as used in the description of reactive and hybrid systems.