On Kleene algebras and closed semirings
MFCS '90 Proceedings on Mathematical foundations of computer science 1990
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
A calculational approach to mathematical induction
Theoretical Computer Science
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Modal Tools for Separation and Refinement
Electronic Notes in Theoretical Computer Science (ENTCS)
Delayed-logic and finite-state machines
FOCS '61 Proceedings of the 2nd Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1961)
Internal axioms for domain semirings
Science of Computer Programming
Automated engineering of relational and algebraic methods in isabelle/hol
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
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We study a weak variant of omega algebra, where one of the usual star induction axioms is absent, in the context of recursive regular equations. We present abstract conditions for explicitly defining the omega operation and use them for proving an algebraic variant of Arden's rule for solving such equations. We instantiate these results in concrete models--languages, traces and relations--showing, for instance, that the omega captures precisely the empty word property in regular languages. Finally, we derive Salomaa's axioms for the algebra of regular events. This yields a sound and complete axiomatisation in which the "regular" axioms are weaker than Kleene algebra.