How 2-QCNF algorithm works?
Aspvall, Plass and Tarjan describe a linear time algorithm determining the truth value of quantified 2CNFs in their paper A linear-time algorithm for testing the truth of certain quantified Boolean formulas. Their algorithm is an extension of the well-known algorithm for solving 2SAT using directed reachability; their initial step is computing the strongly connected components of the implication graph.