The foundations of program verification (2nd ed.)
The foundations of program verification (2nd ed.)
A generalization of Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
On Kleene algebras and closed semirings
MFCS '90 Proceedings on Mathematical foundations of computer science 1990
Relations and graphs: discrete mathematics for computer scientists
Relations and graphs: discrete mathematics for computer scientists
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
ACM Transactions on Programming Languages and Systems (TOPLAS)
Verification of sequential and concurrent programs (2nd ed.)
Verification of sequential and concurrent programs (2nd ed.)
On Hoare logic and Kleene algebra with tests
ACM Transactions on Computational Logic (TOCL)
Dynamic Logic
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
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
Mathematical Structures in Computer Science
Some results in dynamic model theory
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
ACM Transactions on Computational Logic (TOCL)
ACM Transactions on Computational Logic (TOCL)
Electronic Notes in Theoretical Computer Science (ENTCS)
Automated Reasoning in Kleene Algebra
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Domain and Antidomain Semigroups
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
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
The structure of the one-generated free domain semiring
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
Knowledge and games in modal 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
Partial, total and general correctness
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Internal axioms for domain semirings
Science of Computer Programming
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Automated engineering of relational and algebraic methods in isabelle/hol
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Automating algebraic methods in isabelle
ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
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
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
Unifying correctness statements
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
Extended designs algebraically
Science of Computer Programming
Program analysis and verification based on kleene algebra in Isabelle/HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
| Hi-index | 0.00 |
Modal Kleene algebras are Kleene algebras enriched by forward and backward box and diamond operators. We formalise the symmetries of these operators as Galois connections, complementarities and dualities. We study their properties in the associated operator algebras and show that the axioms of relation algebra are theorems at the operator level. Modal Kleene algebras provide a unifying semantics for various program calculi and enhance efficient cross-theory reasoning in this class, often in a very concise pointfree style. This claim is supported by novel algebraic soundness and completeness proofs for Hoare logic and by connecting this formalism with an algebraic decision procedure.