Worst-Case Upper Bound for (1, 2)-QSAT

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The rigorous theoretical analysis of the algorithm for a subclass of QSAT, i.e. (1, 2)-QSAT, has been proposed in the literature. (1, 2)-QSAT, first introduced in SAT'08, can be seen as quantified extended 2-CNF formulas. Until now, within our knowledge, there exists no algorithm presenting the worst upper bound for (1, 2)-QSAT. Therefore in this paper, we present an exact algorithm to solve (1, 2)-QSAT. By analyzing the algorithms, we obtain a worst-case upper bound O(1.4142m), where m is the number of clauses.