  We investigate the class of finite dimensional not necessary associative
algebras that have slowly growing length, that is, for any algebra in this
class its length is less than or equal to its dimension. We show that this
class is considerably big, in particular, finite dimensional Lie algebras as
well as many other important classical finite dimensional algebras belong to
this class, for example, Leibniz algebras, Novikov algebras, and Zinbiel
algebras. An exact upper bounds for the length of these algebras is proved. To
do this we transfer the method of characteristic sequences to non-unital
algebras and find certain polynomial conditions on the algebra elements that
guarantee the slow growth of the length function.
