A system of word equations is independent if the set of solutions changes when any one equation is removed. Given n > 2, what is the size of the largest independent system of equations over n variables?

A related question is the analogous question for the size of test sets. For some language L, a test set is a set of words T ⊂ L such that, if two morphisms are equivalent on T, then they are equivalent on L. What is the size of test sets for bounded languages?

-- JeffreyShallit - 13 Jul 2011