P vs. PSPACE: Is Space Computationally More Powerful Than Time?

A central question in complexity theory is the relationship between the complexity classes P and PSPACE. P encompasses problems solvable in reasonable time, while PSPACE deals with space complexity. The prevailing belief is that PSPACE is larger than P, due to space's reusability unlike time. Proving this requires demonstrating problems in PSPACE unsolvable in polynomial time. The article recounts the 1975 breakthrough by Hopcroft, Paul, and Valiant, showing space's slight advantage over time, but progress stalled. Ryan Williams' work finally broke the deadlock, offering fresh insights into resolving the P vs. PSPACE problem.