50-Year-Old Conjecture on Space vs. Time in Computation Cracked

A central question in complexity theory is the relationship between P and PSPACE, classes encompassing problems solvable in reasonable time and space, respectively. Intuitively, space is a more powerful resource than time because it's reusable. For 50 years, researchers aimed to prove PSPACE is larger than P, meaning some problems are impossible to solve quickly but solvable with limited space. Hopcroft, Paul, and Valiant made a breakthrough in 1975, showing space is slightly more powerful than time. However, this progress was limited by the 'simulation' approach. Ryan Williams finally broke the deadlock with a novel approach, solving the long-standing problem.