About one class polynomial problems with not polynomial certificates

TL;DR

This paper introduces a class of polynomial problems that lack polynomial certificates, focusing on the efficiency of algorithms based on the size of the set used in constructing combinatorial objects.

Contribution

It presents a new class of polynomial problems without polynomial certificates and analyzes algorithm efficiency relative to set size.

Findings

Defined a new class of polynomial problems without polynomial certificates.

Analyzed algorithm efficiency based on the set size parameter.

Constructed combinatorial objects with specific properties.

Abstract

We build a class of polynomial problems with not polynomial certificates. The parameter concerning which are defined efficiency of corresponding algorithms is the number $n$ of elements of the set has used at construction of combinatory objects (families of subsets) with necessary properties.