Core Viewpoint - The article discusses a groundbreaking research by Ryan Williams that challenges the long-held belief in computer science regarding the relationship between time and space in algorithm execution, suggesting that a small amount of computational memory is theoretically more valuable than a large amount of computational time [1][3]. Group 1: Historical Context - In 1965, Juris Hartmanis and Richard Stearns established rigorous mathematical definitions for "time" and "space," providing a common language for researchers to categorize problems into complexity classes [5][6]. - The complexity class P includes problems solvable in reasonable time, while PSPACE includes problems solvable with a reasonable amount of space, with researchers believing PSPACE is significantly larger than P [7][8]. Group 2: Breakthrough in Complexity Theory - For 50 years, researchers struggled to prove that PSPACE is strictly larger than P, facing a fundamental barrier due to the limitations of previous simulation methods [8][9]. - In 2023, James Cook and Ian Mertz overturned a long-standing assumption about memory usage in algorithms, leading to a new algorithm that could solve the tree evaluation problem with significantly less space than previously thought [10][12]. Group 3: Williams' Revolutionary Approach - Ryan Williams recognized that the new algorithm by Cook and Mertz could serve as a universal space compression tool, allowing for the design of a new simulation mechanism that links time and space complexity more effectively [14][15]. - Williams' method involves breaking down the computation process into blocks and transforming it into a tree evaluation problem, optimizing the space complexity to O(√t log t), where t is the total computation time [16].