P-class is a proper subclass of NP-class; and more

TL;DR

This paper explores the mathematical relationship between P and NP classes, revealing that P is a proper distributive sublattice of NP, thus providing new structural insights into computational complexity classes.

Contribution

It introduces the novel concept that P forms a proper distributive sublattice within NP, advancing the understanding of their algebraic structure.

Findings

P is a proper subclass of NP

P forms a proper distributive sublattice of NP

Provides new algebraic perspective on complexity classes

Abstract

We may give rise to some questions related to the mathematical structures of $P$-class and $NP$-class. We have seen that one is a proper subclass of the other. Here we disclose more that $P$- class turns out to be the proper distributive sublattice of the $NP$- class.