A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
A calculational approach to mathematical induction
Theoretical Computer Science
Modal logic
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Commutation, Transformation, and Termination
Proceedings of the 8th International Conference on Automated Deduction
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
ACM Transactions on Computational Logic (TOCL)
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
Automated verification of refinement laws
Annals of Mathematics and Artificial Intelligence
Internal axioms for domain semirings
Science of Computer Programming
Omega algebras and regular equations
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
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Kleene modules and modal Kleene algebras are applied to automatically verify refinement laws for infinite loops and separation of termination. The key concept in this analysis is divergence which, in some models, abstractly characterises that part of a state space from which infinite dynamics is possible. In other models it expresses infinite iteration. Equational axioms for divergence are introduced, and the concept is refined for different contexts. In particular it is related to Lob's formula, which describes termination in modal logics.