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Is it possible to find out a string only having its corresponding suffix array/table and knowing that the string contains only, for instance, letters "f", "g", "r"? If so, how is that possible?

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Sure: the longest stored suffix is the string itself.

In a suffix array, it's particularly easy to find: scan the array for starting index $1$ -- the suffix starting at the first character is, quite obviously, the string itself.

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Understanding the definition of a suffix array will come in handy here.

http://en.wikipedia.org/wiki/Suffix_array

Suffix Array for the string attcatg$.

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So like Raphael Suggested either look for the index 1 string attcatg$ or look for the longest string in that array which is the same if it doesn't store indices but it should store indices as per definition.

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