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
ACM Transactions on Programming Languages and Systems (TOPLAS)
Reachability Analysis of Pushdown Automata: Application to Model-Checking
CONCUR '97 Proceedings of the 8th International Conference on Concurrency Theory
Towards Kleene Algebra with Recursion
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Instrumenting C programs with nested word monitors
Proceedings of the 14th international SPIN conference on Model checking software
Static analysis of programs using omega algebra with tests
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
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
Verification of common interprocedural compiler optimizations using visibly pushdown kleene algebra
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
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Kleene algebra is a great formalism for doing intraprocedural analysis and verification of programs, but it seems difficult to deal with interprocedural analysis where the power of context-free languages is often needed to represent both the program and the property. In the model checking framework, Alur and Madhusudan defined visibly pushdown automata, which accept a subclass of context-free languages called visibly pushdown languages, to do some interprocedural analyses of programs while remaining decidable. We present visibly pushdown Kleene algebra, an extension of Kleene algebra that axiomatises exactly the equational theory of visibly pushdown languages. The algebra is simply Kleene algebra along with a family of implicit least fixed point operators. Some interprocedural analyses of (mutually) recursive programs are possible in this formalism and it can deal with some non-regular properties.