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Murch
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Merged mining: are there any ways to prevent it?

Supporting merged mining allows a cryptocurrency A to improve the security its blockchain (increase the hash rate) by accepting work done on the blockchain of cryptocurrency B through insertion of a hash of a valid A-block.

Is it possible for cryptocurrency B (say Bitcoin) to prevent its blockchain from being used to effectively enhance the security of a rival coin? (I am assuming the 'A'-hash insertion takes place in the coinbase, which is normally used for entropy).