TL;DR
This paper introduces the MEoP problem, which determines the existence of solutions to specific modular equations over primes, illustrating a separation between NP and P complexity classes.
Contribution
The paper defines the MEoP problem and demonstrates its role in distinguishing NP from P through modular equations over primes.
Findings
MEoP problem is decidable for certain modular equations.
The problem's complexity indicates NP is not equal to P.
This work provides a new approach to separating NP and P.
Abstract
We present the MEoP problem that decides the existence of solutions to certain modular equations over prime numbers and show how this separates the complexity class NP from its subclass P
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Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · Advanced Algebra and Logic