Pré-Publication, Document De Travail Année : 2021

Dense Complete Set For NP

Frank Vega
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Résumé

A sparse language is a formal language such that the number of strings of length $n$ is bounded by a polynomial function of $n$. We create a class with the opposite definition, that is a class of languages that are dense instead of sparse. We define a dense language on $m$ as a formal language (a set of binary strings) where there exists a positive integer $n_{0}$ such that the counting of the number of strings of length $n \geq n_{0}$ in the language is greater than or equal to $2^{n - m}$ where $m$ is a real number and $0 < m \leq 1$. We call the complexity class of all dense languages on $m$ as $DENSE(m)$. We prove that there exists an $\textit{NP--complete}$ problem that belongs to $DENSE(m)$ for every possible value of $0 < m \leq 1$.

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Dates et versions

hal-03320440 , version 1 (16-08-2021)
hal-03320440 , version 2 (20-10-2021)

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  • HAL Id : hal-03320440 , version 2

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Frank Vega. Dense Complete Set For NP. 2021. ⟨hal-03320440v2⟩
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