  Active learning of finite automata has been vigorously pursued for the
purposes of analysis and explanation of black-box systems. In this paper, we
study an L*-style learning algorithm for weighted automata over the max-plus
semiring. The max-plus setting exposes a "consistency" issue in the previously
studied semiring-generic extension of L*: we show that it can fail to maintain
consistency of tables, and can thus make equivalence queries on obviously wrong
hypothesis automata. We present a theoretical fix by a mathematically clean
notion of column-closedness. We also present a nontrivial and reasonably broad
class of weighted languages over the max-plus semiring in which our algorithm
terminates.
