Guessing with limited memory
Wasim Huleihel, Salman Salamatian, Muriel Médard · 2017
Suppose that we wish to guess the realization x of a discrete random variable X taking values in a finite set, by asking sequential questions of the form “Is X is equal to x?” exhausting the elements of X until the answer is Yes. [1, 2]. If the distribution of X is known to the guesser, and the guesser has memory of his previous has memory of his previous queries then the best strategy is to guess in decreasing order of probabilities. In this paper, we consider the problem of a memoryless guesser, namely, each new guess is independent of the previous guesses. We consider also the scenario of a guesser with a bounded number of guesses. For both cases we derive the optimal guessing strategies, and show new connections to Rényi entropy.