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What is the state of a clause with one unassigned literal?

  • A.It is satisfied and may be ignored for the rest of the search
  • B.It is conflicting and requires the solver to backtrack
  • C.It is undetermined and provides no information at all
  • D.It is a unit clause and forces that literal true

Answer: D

With every other literal false, the remaining one must be true if the clause is to be satisfied, so the assignment is forced rather than chosen. Cascading such forced assignments is unit propagation, which dominates the run time of a modern solver. The other descriptions apply to different clause states. Distinguishing the four states a clause may be in is the whole of the bookkeeping a satisfiability solver performs.

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