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What is the other name of informed search strategy?

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Which search uses the problem specific knowledge beyond the definition of the problem?
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The BACKTRACKING-SEARCH algorithm in Figure 5.3 has a very simple policy for what to do when a branch of the search fails: back up to the preceding variable and try a different value for it. This is called chronological-backtracking. It is also possible to go all the way to set of variable that caused failure.
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What are the main cons of hill-climbing search?
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Backtracking is based on ____________
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When do we call the states are safely explored?
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