PSPACE refers to the class of decision problems that can be solved by a Turing machine using a polynomial amount of memory, regardless of the time it takes. It is important because it captures a wide range of problems that are feasible in terms of memory but can still be computationally intensive, connecting closely with other complexity classes like P and NP. Understanding PSPACE helps in grasping the limits of what can be computed efficiently and how problems scale with resources.
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