Discussion
What condition must step costs satisfy for uniform cost search to be optimal?
Answer: C
Non-negative costs are needed for correctness and a strictly positive lower bound is needed for completeness, since a sequence of zero cost steps could otherwise be followed forever without the path cost rising. Equal costs are the special case where breadth first suffices, and integrality and boundedness are not required. A condition that rules out an infinite sequence of free actions is easy to overlook and occasionally matters in practice. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.
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