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A number of academic publications nicely describe many aspects of Valgrind's design and implementation. Online copies of all of them, and others, are available on the Valgrind publications page.
The following paper gives a good overview of Valgrind, and explains how it differs from other dynamic binary instrumentation frameworks such as Pin and DynamoRIO.
The following two papers together give a comprehensive description of how most of Memcheck works. The first paper describes in detail how Memcheck's undefined value error detection (a.k.a. V bits) works. The second paper describes in detail how Memcheck's shadow memory is implemented, and compares it to other alternative approaches.
The following paper describes Callgrind.
The following dissertation describes Valgrind in some detail (many of these details are now out-of-date) as well as Cachegrind, Annelid and Redux. It also covers some underlying theory about dynamic binary analysis in general and what all these tools have in common.
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