Why it matters

SAT solvers surprisingly effective on real problems. Understanding shapes constraint solving.

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The architecture

DPLL: backtracking + unit propagation.

CDCL: adds conflict-driven clause learning.

SAT solver evolutionDPLLbacktracking + UPCDCL+ clause learningHeuristicsVSIDS activityModern solvers (MiniSat, CaDiCaL) handle problems intractable in theory
SAT solving evolution.
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How it works end to end

Encoding: convert problem to CNF (conjunctive normal form).

Solvers: MiniSat, Kissat, CaDiCaL open-source.

Applications: hardware verification, planning, dependency resolution.