Real numbers may have infinitely many digits yet admit short, finite descriptions. Can we recover such a description of an unknown number using only comparisons? This question extends classical integer/rational search to richer representations and connects numerical search with exact query learning.
This talk will focus on automatic reals, whose digits are determined by finite automata. For an unknown real with an s-state representation, we obtain a polynomial-time algorithm using O(s^2) comparisons. For this algorithm, we revisit Angluin’s exact learning model, well known in learning theory, and show how automata-learning techniques can be adapted to identify unknown real numbers using only comparison queries.
If time permits, we will discuss other representations, including algebraic numbers.
This is ongoing joint work with Arvind.