Guesswork and Entropy
David W. Malone, Wayne G. Sullivan · IEEE Transactions on Information Theory · 2004
We derive the moments of the guesswork , the number of attempts required to correctly guess the output of a random source, for a source determined by a Markov chain via a large deviations type estimate. These moments are related to the Perron-Frobenius eigenvalue of the matrix formed by element-wise powers of the Markov chain's transition matrix.