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Description

Book Description — P = NP One of the greatest unsolved problems in mathematics and theoretical computer science is the P versus NP problem: Can every problem whose solution can be efficiently verified also be efficiently solved? This book presents an ambitious mathematical investigation into this fundamental question through symbolic logic, formal reasoning, computational complexity theory, and an original theoretical construction designated as Algorithm A_G. By integrating mathematical logic, algorithmic structures, and deductive reasoning, the author develops a proposed framework for examining the relationship between polynomial-time computation and efficient verification. The work explores the logical foundations of computational complexity and the possibility of establishing a formal correspondence between the complexity classes P and NP. Beyond its mathematical implications, this research addresses profound questions concerning the limits of computation, artificial intelligence, mathematical discovery, and the nature of logical knowledge. Written for mathematicians, computer scientists, logicians, researchers, and intellectually curious readers, this book invites rigorous examination of an original approach to one of the seven Millennium Prize Problems. A mathematical exploration of computation, logic, and the boundaries of what can be efficiently solved.