Explain the concept of PSPACE complexity class.

The concept of PSPACE complexity class is a measure of the computational resources required to solve a problem using a deterministic Turing machine with a polynomial amount of space. PSPACE stands for Polynomial Space, and it represents the set of decision problems that can be solved by a Turing machine using a polynomial amount of space.

In PSPACE, the space complexity is measured in terms of the number of cells on the Turing machine's tape that are used during the computation. The time complexity is not a constraint in PSPACE, meaning that the problem can take an exponential amount of time to solve, as long as it can be solved using a polynomial amount of space.

PSPACE includes problems that can be solved by algorithms that use a polynomial amount of space, such as determining the satisfiability of a propositional logic formula, solving certain types of games like chess or Go, and solving various graph problems.

PSPACE is a superset of the class NP, which represents problems that can be verified in polynomial time. This means that any problem in NP can also be solved in PSPACE, but there are problems in PSPACE that are not known to be in NP.

The concept of PSPACE complexity class is important in the field of automata theory as it helps classify problems based on their space requirements and provides insights into the inherent complexity of solving certain computational problems.