Iteration theories: the equational logic of iterative processes
Iteration theories: the equational logic of iterative processes
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Heterogeneous relation algebra
Relational methods in computer science
MPC '00 Proceedings of the 5th 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
Unifying theories of programming that distinguish nontermination and abort
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Untyping typed algebraic structures and colouring proof nets of cyclic linear logic
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Verification of pushdown systems using omega algebra with domain
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
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Recasting hoare and he's unifying theory of programs in the context of general correctness
IW-FM'01 Proceedings of the 5th Irish conference on Formal Methods
Extended designs algebraically
Science of Computer Programming
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We propose axioms for 1-free omega algebra, typed 1-free omega algebra and typed omega algebra. They are based on Kozen's axioms for 1-free and typed Kleene algebra and Cohen's axioms for the omega operation. In contrast to Kleene algebra, several laws of omega algebra turn into independent axioms in the typed or 1-free variants. We set up a matrix algebra over typed 1-free omega algebras by lifting the underlying structure. The algebra includes non-square matrices and care has to be taken to preserve type-correctness. The matrices can represent programs in total and general correctness. We apply the typed construction to derive the omega operation on two such representations, for which the untyped construction does not work. We embed typed 1-free omega algebra into 1-free omega algebra, and this into omega algebra. Some of our embeddings, however, do not preserve the greatest element. We obtain that the validity of a universal formula using only +, ċ, +, ω and 0 carries over from omega algebra to its typed variant. This corresponds to Kozen's result for typed Kleene algebra.