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)
On Hoare logic and Kleene algebra with tests
ACM Transactions on Computational Logic (TOCL)
Dynamic Logic
Kleene Algebra with Tests: Completeness and Decidability
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
Dynamic algebras and the nature of induction
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Automata on Guarded Strings and Applications
Automata on Guarded Strings and Applications
Kleene Algebra with Tests and Program Schematology
Kleene Algebra with Tests and Program Schematology
Intuitionistic Linear Logic and Partial Correctness
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Algebras of modal operators and partial correctness
Theoretical Computer Science - Algebraic methodology and software technology
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
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
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First-order structures over a fixed signature Σ give rise to a family of trace-based and relational Kleene algebras with tests defined in terms of Tarskian frames. A Tarskian frame is a Kripke frame whose states are valuations of program variables and whose atomic actions are state changes effected by variable assignments x := e, where e is a Σ-term. The Kleene algebras with tests that arise in this way play a role in dynamic model theory akin to the role played by Lindenbaum algebras in classical first-order model theory. Given a first-order theory T over Σ, we exhibit a Kripke frame U whose trace algebra TrU is universal for the equational theory of Tarskian trace algebras over Σ satisfying T, although U itself is not Tarskian in general. The corresponding relation algebra RelU is not universal for the equational theory of relation algebras of Tarskian frames, but it is so modulo observational equivalence.