On Kleene algebras and closed semirings
MFCS '90 Proceedings on Mathematical foundations of computer science 1990
Logic and information flow
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)
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Toward Solving Equations in Kleene Algebras
Proceedings of the 2007 conference on New Trends in Software Methodologies, Tools and Techniques: Proceedings of the sixth SoMeT_07
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This work aims to investigate conditions under which program analysis can be viewed as algebraically solving equations involving terms of subclasses of Kleene algebras and variables. In this paper, we show how to solve a kind of linear equations in which variables appear only on one side of the equality sign, over a *-continuous action lattice. Furthermore, based on the method developed for solving equations, we present how model checking of a restricted version of the linear µ-calculus over finite traces can be done by algebraic manipulations. Finally, we give some ideas on how to extend the resolution method to other classes of equations and algebraic structures.