This paper develops a formal definition of Minimal Search to evaluate the idea that Agree and Labeling could be reduced to Minimal Search. Different aspects of the search algorithm in Minimal Search, i.e., breadth-first vs. depth-first search, parallel vs. serial search, global vs. modular search are compared, and reasons for choosing between each of these pairs are given based on detailed examinations of their theoretical and empirical consequences. This paper argues, based on the formal definition of Minimal Search, that Agree and Labeling can only be partially unified by Minimal Search: the search algorithms in Agree and Labeling can be unified by Minimal Search, but the values of the search targets and search domains are determined by Agree and Labeling independently. This paper (re)defines Agree and Labeling based on Minimal Search to capture both the similarities and differences between these two operations.

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