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I've been given the following question as a homework:

If h is consistent, then A* - CSCS will expand at most as many nodes as A* graph search.

English not being my native language, I'm kind of struggling to understand the true meaning of the text in bold in the context of this sentence.

From what I understand, A* - CSCS will always expand fewer or the same amount of nodes then A* graph search. That is, the number of nodes that A* graph search expands will always be larger or equal to the number of nodes that A* - CSCS expands.

Is this correct?

Sorry for bringing out the question involving mathematics. What I need is a linguistic explanation of the sentence, not help in mathematics.

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closed as general reference by FumbleFingers, MετάEd, Cameron, Matt E. Эллен, StoneyB Oct 6 '12 at 19:28

This question is too basic; it can be definitively and permanently answered by a single link to a standard internet reference source designed specifically to find that type of information.If this question can be reworded to fit the rules in the help center, please edit the question.

It's probably the lack of commas that's throwing you off: If h is consistent, then A* - CSCS will expand, at most, as many nodes as A* graph search. – coleopterist Oct 3 '12 at 16:34
General Reference - at most = up to, but not more than, and as many X as... = the same number of X as... – FumbleFingers Oct 3 '12 at 16:35
up vote 10 down vote accepted

You are correct.

Read it this way:

If h is consistent, then at most A* - CSCS will expand as many nodes as A* graph search.

Or, more naturally:

If h is consistent, then A* - CSCS will not expand any more nodes than A* graph search.

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Yes, your understanding is correct. At most as many as can usually be replaced by no more than; I don't know why the author chose this unusual form of words.

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Because discussions of algorithms often include their bounding conditions, "at most" is the usual way of expressing it, while "no more than" can be confusing. In this case, the bounding condition is best expressed as equivalent to another well-understood condition, and therefore the two phrases are juxtaposed in a construction that is odd for English, but correct for the mathematical formulation. – shipr Oct 3 '12 at 17:39

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