We define a new heuristic h DS for ASP, and implement it in the (disjunctive) ASP system DLV. The new heuristic improves the evaluation of Σ P 2 /Π P 2hard ASP programs while maintaining the benign behaviour of the well-assessed heuristic of DLV on NP problems. We experiment with the new heuristic on QBFs. h DS significantly outperforms the heuristic of DLV on hard 2QBF problems. We compare also the DLV system (with the new heuristic h DS ) to three prominent QBF solvers. The results of the

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... arison, performed on instances used in the last QBF competition, indicate that ASP systems can be faster than QBF systems on Σ P 2 /Π P 2 -hard problems.