*-Continuous Kleene $\omega$-Algebras
نویسندگان
چکیده
We define and study basic properties of ∗-continuous Kleene ω-algebras that involve a ∗-continuous Kleene algebra with a ∗-continuous action on a semimodule and an infinite product operation that is also ∗-continuous. We show that ∗-continuous Kleene ω-algebras give rise to iteration semiring-semimodule pairs. We show how our work can be applied to solve certain energy problems for hybrid systems.
منابع مشابه
*-Continuous Kleene $\omega$-Algebras for Energy Problems
Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on ∗-continuous Kleene ω-algebras, we show here that energy problems can be solved by algebraic manipulations on the transition matrix of energy automata. To this end, we prove general results about certain classes of finitely additive functions on complete lattices which should be of a ...
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Typed omega algebras extend Kozen’s typed Kleene algebras by an operation for infinite iteration in a similar way as Cohen’s omega algebras extend Kleene algebras in the untyped case. Typing these algebras is motivated by non-square matrices in automata constructions and applications in program semantics. For several reasons – the theory of untyped (Kleene or omega) algebras is well developed, ...
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