Time complexity of minimizing Boolean expression Given any arbitrary boolean expression using AND, OR and NOT gates what is the time complexity of minimizing the expression such that minimum number of gates are used.

The following Wikipedia article only talks about the space complexity of the problem (which is PSPACE), but does not talks about the time complexity.

https://en.wikipedia.org/wiki/Circuit_minimization_for_Boolean_functions
The Wikipedia article states that the problem is $\Sigma_2^P$-hard, and in particular it's NP-hard. Therefore it's probably not solvable in polynomial time (unless P=NP).