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It is shown that the compressed word problem for an HNN-extension 〈H,t∣t −1 at=ϕ(a) (a∈A)〉 with A finite is polynomial time Turing-reducible to the compressed word problem for the base group H. An analogous result for amalgamated free products is shown as well.

Compressed Word Problems in HNN-Extensions and Amalgamated Products