A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Ordered chaining calculi for first-order theories of transitive relations
Journal of the ACM (JACM)
Evaluating general purpose automated theorem proving systems
Artificial Intelligence
Refinement Calculus: A Systematic Introduction
Refinement Calculus: A Systematic Introduction
Journal of Automated Reasoning
A Method for Refining Atomicity in Parallel Algorithms
PARLE '89 Proceedings of the Parallel Architectures and Languages Europe, Volume II: Parallel Languages
From Kleene Algebra to Refinement Algebra
MPC '02 Proceedings of the 6th International Conference on Mathematics of Program Construction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
leanCoP: lean connection-based theorem proving
Journal of Symbolic Computation - Special issue: First order theorem proving
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
AI Communications
Intelligent Systems and Formal Methods in Software Engineering
IEEE Intelligent Systems
AI Communications - CASC
The design and implementation of VAMPIRE
AI Communications - CASC
AI Communications - CASC
Electronic Notes in Theoretical Computer Science (ENTCS)
The CADE-21 automated theorem proving system competition
AI Communications
Modal Tools for Separation and Refinement
Electronic Notes in Theoretical Computer Science (ENTCS)
Data Refinement: Model-Oriented Proof Methods and their Comparison
Data Refinement: Model-Oriented Proof Methods and their Comparison
Diagram Chase in Relational System Development
Electronic Notes in Theoretical Computer Science (ENTCS)
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
Geometric resolution: a proof procedure based on finite model search
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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
Automating algebraic methods in isabelle
ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
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Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs.