De Bruijn Sequence - Uses

Uses

The sequence can be used to shorten a brute-force attack on a PIN-like code lock that does not have an "enter" key and accepts the last n digits entered. For example, a digital door lock with a 4-digit code would have B(10, 4) solutions, with length 10,000. Therefore, only at most 10,000 + 3 = 10,003 (as the solutions are cyclic) presses are needed to open the lock. Trying all codes separately would require 4 × 10,000 = 40,000 presses.

The symbols of a De Bruijn sequence written around a circular object (such as a wheel of a robot) can be used to identify its angle by examining the n consecutive symbols facing a fixed point. Gray codes can be used as similar rotary positional encoding mechanisms.

De Bruijn cycles are of general use in neuroscience and psychology experiments that examine the effect of stimulus order upon neural systems, and can be specially crafted for use with functional magnetic resonance imaging.

A De Bruijn sequence can be used to quickly find the first or last bit in a word.

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