Ideal Stream Algebra

Möller, Bernhard

doi:10.1007/3-540-49254-2_3

Cited by 7 publications

(4 citation statements)

References 37 publications

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“…We have seen that it is possible to integrate non-strictness with finite and infinite iteration as well as with modal operators. This framework allows, for instance, an abstract and more concise reworking of the stream applications treated in [24]; this will be the subject of further papers. Let us briefly sketch two other interesting applications of the theory.…”

Section: Discussionmentioning

confidence: 99%

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Kleene getting lazy

Möller

2007

Science of Computer Programming

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We propose a relaxation of Kleene algebra by giving up strictness and right-distributivity of composition. This allows the subsumption of Dijkstra's computation calculus, Cohen's omega algebra and von Wright's demonic refinement algebra. Moreover, by adding domain and codomain operators we can also incorporate modal operators. We show that predicate transformers form lazy Kleene algebras, the disjunctive and conjunctive ones even lazy omega Kleene algebras. We also briefly sketch two further applications: a modal lazy Kleene algebra of commands modelling total correctness and another one that abstractly characterizes sets of trajectories as used in the description of reactive and hybrid systems.

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Section: Discussionmentioning

confidence: 99%

“…While finite iteration suffices for safety analysis of infinite computations [21], infinite iteration is useful for describing liveness aspects (see e.g. [24]). It has been studied intensively in the theory of ω-languages [33].…”

Section: Iteration -Lazy Kleene and Omega Algebrasmentioning

confidence: 99%

Kleene getting lazy

Möller

2007

Science of Computer Programming

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“…We have seen that it is possible to integrate non-strictness with finite and infinite iteration as well as with modal operators. This framework allows, for instance, an abstract and more concise reworking of the stream applications treated in [17]; this will be the subject of further papers. But hopefully the framework will have many more applications.…”

Section: Discussionmentioning

confidence: 99%

“…While safety analysis of infinite computations is also possible using star only [14], omega iteration serves to describe liveness aspects (see e.g. [17]). Definition 6.1 A left or lazy Kleene algebra (LKA) is a structure (K, * ) such that K is an IL-semiring and the star * satisfies, for a, b, c ∈ K, the unfold and induction laws…”

Section: Iteration -Lazy Kleene Algebrasmentioning

confidence: 99%

Lazy Kleene Algebra

Möller

2004

Lecture Notes in Computer Science

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We propose a relaxation of Kleene algebra by giving up strictness and right-distributivity of composition. This allows the subsumption of Dijkstra's computation calculus, Cohen's omega algebra and von Wright's demonic refinement algebra. Moreover, by adding domain and codomain operators we can also incorporate modal operators. Finally, it is shown that predicate transformers form lazy Kleene algebras again, the disjunctive and conjunctive ones even lazy Kleene algebras with an omega operation.

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Transforming Stream Processing Functions into State Transition Machines

Dosch

Stümpel

2006

Software Engineering Research and Applications

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Ideal Stream Algebra

Cited by 7 publications

References 37 publications

Kleene getting lazy

Kleene getting lazy

Lazy Kleene Algebra

Transforming Stream Processing Functions into State Transition Machines

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