On Optimal T-Adic Representations

In this paper, an efficient algorithm for generating all optimal r-adic representations of a T-adic integer is presented. Our approach is to use a nondeterministic finite automaton (NFA) to produce all T-adic representations at first, and then combined with Floyd algorithm, we get the upper bound of optimal radic representations´ length and some prerequisites used in the generating process of optimal representations. Meanwhile, the exact number of optimal T-adic representations can also be obtained efficiently.