Some results in dynamic model theory
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
On the representation of kleene algebras with tests
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
An axiomatization of arrays for kleene algebra with tests
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
Local variable scoping and kleene algebra with tests
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
Kleene algebra with tests and coq tools for while programs
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Program analysis and verification based on kleene algebra in Isabelle/HOL
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
NetKAT: semantic foundations for networks
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
| Hi-index | 0.00 |
The theory of flowchart schemes has a rich history going back to Ianov (1960); see Manna (1974) for an elementary exposition. A central question in the theory of program schemes is scheme equivalence. Manna presents several examples of equivalence proofs that work by simplifying the schemes using various combinatorial transformation rules. In this paper we present a purely algebraic approach to this problem using Kleene algebra with tests (KAT). Instead of transforming schemes directly using combinatorial graph manipulation, we regard them as a certain kind of automaton on abstract traces. We prove a generalization of Kleene''s theorem and use it to construct equivalent expressions in the language of KAT. We can then give a purely equational proof of the equivalence of the resulting expressions. We prove soundness of the method and give a detailed example of its use.