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Why does propagation always terminate?

  • A.Domains only shrink and are finite in size
  • B.The number of constraints is bounded in advance
  • C.Each propagator is called at most once per variable
  • D.A limit on the number of iterations is imposed

Answer: A

Since every propagation step removes at least one value from a finite domain and nothing is ever added, the process cannot continue indefinitely. That monotonicity is what makes the fixed point well defined. Constraint counts, call limits and iteration caps are implementation details rather than the reason. Establishing termination from a decreasing finite measure is the standard argument for any such algorithm and it is worth constructing rather than assuming.

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