GRASP (SAT solver)

Conflict-Driven Clause Learning (CDCL) is a highly effective algorithm used in modern Boolean Satisfiability (SAT) solvers. It forms the core of many state-of-the-art solvers, including GRASP. CDCL's power stems from its ability to efficiently explore the search space of possible truth assignments for Boolean variables, leveraging learned information from conflicts to prune unproductive branches.

The algorithm works by iteratively assigning truth values to variables, guided by a decision heuristic (often based on variable occurrence frequency). If an assignment leads to a conflict (a clause becomes false), the solver performs a process called ''conflict analysis''. This analysis identifies the reasons for the conflict and derives a new clause, called a ''learned clause'', that prevents the same conflict from occurring again. This learned clause is added to the problem's constraint set.

The process of conflict analysis involves a ''backtracking'' step, where the solver undoes some of its previous assignments. The amount of backtracking is determined by the ''Unique Implication Point'' (UIP) analysis, which helps to find a suitable point to backtrack to while still learning an effective clause. This careful selection of backtracking level ensures efficient pruning of the search space.

The efficiency of CDCL stems from several key aspects:

• Efficient Boolean Constraint Propagation (BCP): CDCL uses BCP to quickly deduce the implications of assignments and detect conflicts early.
• Effective Heuristics: Sophisticated heuristics for variable selection and decision making significantly impact performance.
• Clause Learning: The ability to learn clauses from conflicts allows the solver to dynamically adapt its search strategy and avoid repeated exploration of unsuccessful branches.
• Restarts: Periodic restarts can help escape local optima in the search space.

CDCL solvers, such as GRASP, are crucial for solving large and complex SAT problems arising in various domains, including hardware and software verification, artificial intelligence, and operations research. The ongoing development of improved heuristics and techniques for conflict analysis continues to push the boundaries of what is solvable with SAT solvers.