Abstract
In this chapter, we introduce the main topic of this book, namely the compressed word problem for a finitely generated group. This is the variant of the word problem, where the input word is not written down explicitly, but given by an SLP. Since the input word is given in a more succinct way, the compressed word problem for a group G may have a higher computational complexity than the word problem for G, and in Sect. 4.8 we will see such a group.
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