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It investigates the resources, such as time, space, and randomness, required to solve computational problems. This field plays a crucial role in identifying problems that cannot be efficiently solved and categorizing them into complexity classes, which provide a framework for classifying problems based on their level of difficulty. The Wikipedia page on computational complexity theory provides a comprehensive overview of this area. It covers various topics, including the basics of computational complexity, such as the definitions of time and space complexity, as well as the notion of polynomial-time algorithms. The page discusses different complexity classes, such as P, NP, and NP-complete, and explores the relationships between them, including the famous P vs. NP question, which asks whether the set of problems that can be solved quickly (P) is the same as the set of problems for which solutions can be quickly verified (NP). Furthermore, the page addresses the significance of computational complexity theory in everyday life, particularly its impact on fields like cryptography, optimization, and artificial intelligence. It explores the applications of complexity classes in designing secure cryptographic protocols, developing efficient algorithms for optimization problems, and understanding the inherent difficulty of various computational tasks. Moreover, the page delves into the mathematical foundations of computational complexity theory, including formal models of computation and complexity measures, such as time and space complexity. It provides historical context by discussing the contributions of renowned researchers and landmark results that have shaped the field. Additionally, the Wikipedia page highlights open questions and ongoing research in computational complexity theory, such as the exploration of the complexity of quantum computing and the development of complexity classes beyond P and NP. It acknowledges the interdisciplinary nature of the field, where researchers from computer science, mathematics, and other disciplines collaborate to advance our understanding of computational limits. Overall, the Wikipedia page on computational complexity theory serves as a valuable resource for anyone seeking to learn about the theoretical foundations of computer science and the fundamental considerations in solving computational problems efficiently.