SMT-Solver can be used for constraint solving. As we known, CSP solvers are also for constraint solving for many years. So what's the advantage of SMT-solver over CSP solvers?
What's the advantage of SMT-solver over CSP-solver in constraint solving?
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That entirely depends on what you want to do. You can translate both to SAT and solve constraint problems as a SAT problem. Constraint solvers usually offer the highest level of abstraction when it comes to modelling the problem. SAT solvers are very fast, but depending on your problem an SMT or constraint solver might be faster.
There is no general answer to your question. It depends on your particular use case.