COMPUTATIONAL COMPLEXITY AND THE LIMITS OF COMPUTATION

This study compares computational complexity and computation limits methods. The study compares and evaluates complicated computational problem-solving methods. Algorithmic design, complexity analysis, reductions, approximation algorithms, randomised algorithms, and cryptography analysis are included. Comparative studies examine theoretical basis, actual implementations, and empirical evaluations of various strategies. This study analyses the strategies to identify their strengths and weaknesses. Each technique is assessed for computing efficiency, scalability, robustness, and applicability to different problem areas. Algorithmic complexity, problem complexity, and real-world restrictions are considered while examining approach trade-offs. The comparative analysis helps researchers, practitioners, and decision-makers understand existing techniques and choose relevant approaches for specific computing difficulties. Computational complexity theory, efficient algorithms, optimisation methodologies, and secure computational systems benefit from the study