Hi @Sundarappan Kathiresan, how are you? Thanks for reading the article. I hope you enjoying.

As the statement of expression, the given condition is that f(x) = f(y) if and only if x = y xor a. Here the value of a is unknown and we need to identify or solve the a, in the situation we call it as hidden string. From the example or fig 5, the occurance of the same value is periodic in nature means it is repeating with a pattern or hidden pattern, the pattern here we call it is as a period. For your reference sharing a wiki article which we can consider as an example. https://en.wikipedia.org/wiki/Periodic_function