Deterministic SAT solver

Question

I have the following question. Is the SAT solvers are deterministic?

I mean, for example, about miniSAT and DPLL algorithm. Are they completely deterministic?

If these algorithms will return unSAT it means that certainly the solution does not exist?

Answer 1

Satisfiability (of systems of propositional formulae) is a decidable problem. The relevant SAT solving algorithms like DPLL are complete: they always terminate with a correct yes/no answer about satisfiability. SAT solver implementations should always either return a correct answer or run out of time or memory or some other resource (like the user's patience). An implementation might be non-deterministic about its failure or termination modes, but if it runs to completion with an answer, the implementor would consider it to be a bug if the answer was unSAT for a satisfiable system or SAT for an unsatisfiable system. If you want more details, I suggest you ask for more information on computer science stack exchange or on forums for particular SAT solvers of interest to you.