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Infinite Spectra of First-Order Properties for Random Hypergraphs

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Abstract

We study the asymptotic behavior of probabilities of first-order properties for random uniform hypergraphs. In 1990, J. Spencer introduced the notion of a spectrum for graph properties and proved the existence of a first-order property with an infinite spectrum. In this paper we give a definition of a spectrum for properties of uniform hypergraphs and establish an almost tight bound for the minimum quantifier depth of a first-order formula with infinite spectrum.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    S. N. Popova

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  1. S. N. Popova
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Correspondence to S. N. Popova.

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Original Russian Text © S.N. Popova, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 3, pp. 92–101.

The research was carried out at the expense of the Russian Science Foundation, project no. 16-11-10014.

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Popova, S.N. Infinite Spectra of First-Order Properties for Random Hypergraphs. Probl Inf Transm 54, 281–289 (2018). https://doi.org/10.1134/S0032946018030079

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  • DOI: https://doi.org/10.1134/S0032946018030079

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