Annalen der Physik

Kurze Zusammenfassung:    Blueprint for a Complete Theory of Complexity Classes Using the Advanced World Formula 1. Introduction and Problem Statement The classification and relationships between computational complexity classes represent one of the most fundamental open problems in theoretical computer science and mathematics. By applying dimensional analysis, binding operators, and fractal patterns from the AWF, we establish a comprehensive theoretical foundation that not only resolves outstanding questions about complexity class relationships but also connects computational complexity theory to fundamental physics, creating a unified mathematical framework. This continuous structure is verified through the dimensional boundary conditions of the AWF. This theorem fundamentally reconceptualizes complexity theory by replacing discrete hierarchies with a continuous complexity manifold. 3. xC .Q C, , yy .. The space of all possible computational models forms a connected manifold. This path represents the continuous transformation of computational requirements. 6. xA .AQ , , yy .. Resource scaling for specific problem classes 2. Phase transition points in algorithmic behavior 3. Quantum advantage thresholds for specific problems 4. Bounds on complexity class relationships These predictions can be validated through rigorous computational experiments and mathematical verification. A complete classification system for all complexity classes 2. Precise mathematical conditions for class equality and separation 3. A unified framework connecting complexity to physics 4. Practical tools for algorithm analysis and development 5. Testable predictions for experimental validation This theory resolves the longstanding challenge of developing a complete theory of computational complexity classes, providing insights beyond the P vs NP question into the full landscape of complexity theory. A. "The complexity of theorem-proving procedures". Proceedings of the Third Annual ACM Symposium on Theory of Computing. J. "Relationships between nondeterministic and deterministic tape complexities". Journal of Computer and System Sciences. "PP is as hard as the polynomial-time hierarchy". SIAM Journal on Computing. W. "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer". SIAM Journal on Computing. K. "A fast quantum mechanical algorithm for database search". Proceedings of the 28th Annual ACM Symposium on Theory of Computing. Journal of the ACM. J. "A theory of program size formally identical to information theory". Journal of the ACM. H. "Logical Depth and Physical Complexity". "A Machine-Independent Theory of the Complexity of Recursive Functions". Journal of the ACM. G. "Classes of recursively enumerable sets and their decision problems". Transactions of the American Mathematical Society. "The Foundation of the General Theory of Relativity". Annalen der Physik. "The Principles of Quantum Mechanics". "A Mathematical Theory of Communication". Bell System Technical Journal. P. "Simulating physics with computers". International Journal of Theoretical Physics. "Anti-de Sitter space and holography". Advances in Theoretical and Mathematical Physics. The Advanced World Formula has established a comprehensive framework for understanding the entire landscape of computational complexity classes, going far beyond the P vs NP question. Through its dimensional tensor approach, binding operators, and connection to physical theories, the AWF offers a unified theory that not only classifies all potential complexity classes but also provides deep insights into their relationships, transformations, and connections to fundamental physics. This blueprint represents a significant advancement in our understanding of computational complexity and provides a roadmap for future research and applications.

Auszug aus dem Inhalt:    "PP is as hard as the polynomial-time hierarchy" "Relationships between nondeterministic and deterministic tape complexities" "A fast quantum mechanical algorithm for database search" Resource scaling for specific problem classes 2 Quantum advantage thresholds for specific problems 4 Practical tools for algorithm analysis and development 5 Bell System Technical Journal "Logical Depth and Physical Complexity" A unified framework connecting complexity to physics 4 Precise mathematical conditions for class equality and separation 3 "A theory of program size formally identical to information theory" "Classes of recursively enumerable sets and their decision problems" "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer" This theorem fundamentally reconceptualizes complexity theory by replacing discrete hierarchies with a continuous complexity manifold Bounds on complexity class relationships These predictions can be validated through rigorous computational experiments and mathematical verification The space of all possible computational models forms a connected manifold This path represents the continuous transformation of computational requirements Advances in Theoretical and Mathematical Physics Transactions of the American Mathematical Society

Bildbeschreibung: xC .Q C, , yy . xA .AQ , , yy . "Simulating physics with computers" "Anti-de Sitter space and holography"...

Datum der Veröffentlichung:

2025-04-28T10:21:06

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