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Untying of Clutter-Family Supports and Its Role in the Monotone-Structure Reliability Theory

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Abstract

We suggest a transformation of supports of a clutter family. It is a natural generalization of the untying transformation of a one-clutter support previously introduced by the author. We show that the new transformation does not decrease the reliability of the corresponding clutter sum. We give new bounds for the clutter-sum reliability. We demonstrate that the untying transformation of clutter-family supports and the factor transformation introduced by McDiarmid provide a combinatorial basis for the monotone-structure reliability theory.

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  1. V. P. Polesskii
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Polesskii, V.P. Untying of Clutter-Family Supports and Its Role in the Monotone-Structure Reliability Theory. Problems of Information Transmission 37, 140–154 (2001). https://doi.org/10.1023/A:1010422108958

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  • DOI: https://doi.org/10.1023/A:1010422108958

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