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What is a fixed point in constraint propagation?

  • A.The point at which the search has assigned every variable
  • B.The value at which a variable's own domain becomes a singleton
  • C.The moment at which the first constraint becomes satisfied
  • D.The state in which no propagator can remove any further value

Answer: D

Propagation runs until no propagator can make any further deduction, and that fixed point is the state in which search resumes. Reaching it is guaranteed because domains only shrink and are finite. Complete assignment, singleton domains and individual satisfaction are different events. An iterative process guaranteed to terminate because a finite quantity decreases monotonically is a pattern worth recognising, since it makes the termination argument immediate.

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