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2008•Electronic Notes in Theoretical Computer ScienceOpen access

Liveness in Interaction Systems

Mila Majster-Cederbaum, Moritz Martens, Christoph Minnameier

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Abstract

Interaction systems were proposed and implemented by Sifakis et al. as a model for the design and study of component based systems. We investigate here the property of liveness in interaction systems where liveness of an action, a component or a set of components means that the action (component, set of components) will repeatedly participate in every run of the global system. We show that deciding liveness is NP-hard. Then we present a characterization of liveness. Finally, by exploiting local information, we establish a polynomial-time criterion that guarantees liveness. We combine the criterion with the characterization to obtain a test for liveness.

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What this paper is about

Interaction systems were proposed and implemented by Sifakis et al. as a model for the design and study of component based systems. We investigate here the property of liveness in interaction systems where liveness of an action, a component or a set of components means that the action (component, set of components) will repeatedly participate in every run of the global system. We show that deciding liveness is NP-hard. Then we present a characterization of liveness. Finally, by exploiting local information, we establish a polynomial-time criterion that guarantees liveness. We combine the criterion with the characterization to obtain a test for liveness.

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Available abstract

Interaction systems were proposed and implemented by Sifakis et al. as a model for the design and study of component based systems. We investigate here the property of liveness in interaction systems where liveness of an action, a component or a set of components means that the action (component, set of components) will repeatedly participate in every run of the global system. We show that deciding liveness is NP-hard. Then we present a characterization of liveness. Finally, by exploiting local information, we establish a polynomial-time criterion that guarantees liveness. We combine the criterion with the characterization to obtain a test for liveness.

Key concepts: Liveness, Component (thermodynamics), Computer science, Set (abstract data type), Property (philosophy), Characterization (materials science), Action (physics), Theoretical computer science

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