Algorithms and Complexity

Algorithms are step-by-step procedures or formulas for solving problems, often used in computer science. Complexity, in this context, refers to the resources (like time and space) an algorithm uses as the size of the input grows. Proof Theory studies the structure and foundations of mathematical reasoning. In this framework, understanding the efficiency of algorithms helps determine which problems can be solved effectively, and how quickly, shedding light on what is computationally feasible versus what remains unsolvable. This interplay helps establish the limits of computation and enhances our understanding of problem-solving processes.