Realtime Online Solving of Quantified CSPs

Abstract

Abstract. We define Realtime Online solving of Quantified Constraint Satisfaction Problems (QCSPs) as a model for realtime online CSP solving. We use a combination of propagation, lookahead and heuristics and show how all three improve performance. For adversarial opponents we show that we can achieve promising results through good lookahead and heuristics and that a version of alpha beta pruning performs strongly. For random opponents, we show that we can frequently achieve solutions even on problems which lack a winning strategy and that we can improve our success rate by using Existential Quantified Generalised Arc Consistency, a lower level of consistency than SQGAC, to maximise pruning without removing solutions. We also consider the power of the universal opponent and show that through good heuristic selection we can generate a significantly stronger player than a static heuristic provides.

Preferred Explanations for Quantified Constraint Satisfaction Problems

“…Using an incomplete operator is perfectly reasonable since it only means that the conflict computed is minimal with respect to the consistency operator. Furthermore, some interesting classes of QCSP may be easy to solve in practice despite the worst-case theoretical complexity, e.g., the QCSPs solved in [5].…”

Compilation for QCSP

“…Most of the recent decision procedure for QCSP [3,5,12,7] are based on a search algorithm (except [18] which is based on a bottom-up approach and [13] which is based on a translation to quantified boolean formulas) and off-line procedures (except [2] which is an on-line real-time algorithm based on Monte Carlo game tree search and [17] which is based on standard game tree search techniques). Such an algorithm chooses a variable, branches on the different values of the domain, verifies if the subproblems have some solutions and combines, according to the semantics of the quantifier associated to the variable, those solutions into a solution to the problem.…”