Bridging Constraint Satisfaction and Boolean Satisfiability by Justyna Petke

By Justyna Petke

This booklet presents an important step in the direction of bridging the parts of Boolean satisfiability and constraint delight by means of answering the query why SAT-solvers are effective on definite sessions of CSP situations that are demanding to unravel for traditional constraint solvers. the writer additionally supplies theoretical purposes for selecting a specific SAT encoding for numerous very important sessions of CSP instances.

Boolean satisfiability and constraint delight emerged independently as new fields of machine technology, and diversified fixing options became regular for challenge fixing within the parts. although any propositional formulation (SAT) should be seen as an example of the overall constraint delight challenge (CSP), the consequences of this connection have basically been studied within the previous few years.

The e-book can be important for researchers and graduate scholars in synthetic intelligence and theoretical computing device technology.

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Hence SAT-solvers usually implement some mechanism for removing redundant conflict clauses. BerkMin [GN02] solver counts the number of conflicts each clause has been involved in recently. Another heuristic deletes clauses that contain many non-false literals [BS97]. 5 Hybrid solvers and SMT-solvers SAT-solvers can actually be used for deciding the satisfiability of CSP instances. Such SAT-based solvers first translate the input instance into SAT and then use a SAT-solver. We will call such solvers SAT-based constraint solvers.

If one is found that is different from the other watched literal, the process continues. If the only choice is the other watched literal, then it is set to True if it has not already been assigned that value. If no non-false literal is found, then the clause is conflicting. The good thing about this approach is that during backtracking the pointers are not changed. This is because the literals being watched are the last to be assigned to False, so at backtracking they will become unassigned and hence can still be watched.

In the experimental results recorded here we ask the solvers to solve the search problem. The time complexity of this search problem is at most exponential in the size of the input, since the size of the total search space for possible solutions is jDjjVj . Moreover, if we assume that each constraint is represented in such a way that checking whether a given assignment satisfies a given constraint can be completed in polynomial-time, then CSP clearly belongs to the problem class NP, since an 1 DIMACS CNF is the standard input format for encoding CNF formulae.

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