Infinite Spectra of First-Order Properties for Random Hypergraphs

Infinite Spectra of First-Order Properties for Random Hypergraphs

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...

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Veröffentlicht in:Problems of information transmission 2018-07, Vol.54 (3), p.281-289
1. Verfasser: Popova, S. N.
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Communications Engineering
Control
Electrical Engineering
Engineering
Graph theory
Graphs
Information Storage and Retrieval
Large Systems
Networks
Systems Theory
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Zusammenfassung: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.
ISSN:0032-9460
1608-3253
DOI:10.1134/S0032946018030079