One of the fundamental ways to construct De Bruijn sequences is by using a shift-rule. A shift-rule receives a word as an argument and computes the digit that appears after it in the sequence. An optimal shift-rule for an (n, k)-De Bruijn sequence runs in time O(n). We propose an extended notion we name a generalized-shift-rule, which receives a word, w, and an integer, c, and outputs the c dig...

A decision-theoretic framework is described for sequential classification when the parameter space is a finite partially ordered set. An example of an optimal strategy is then presented. This example establishes that an asymptotically optimal class of experiment selection rules is not necessarily optimal in the given decision-theoretic setting.

A general theorem on asymptotically optimal sequential selection of experiments is presented and applied to a Bayesian classification problem when the parameter space is a finite partially ordered set. The main results include establishing conditions under which the posterior probability of the true state converges to one almost surely, and determining optimal rates of convergence. Properties o...