Let $$w$$ be any string of length $$n$$ in $${\left\{ {0,1} \right\}^ * }$$. Let $$L$$ be the set of all substrings of $$w.$$ What is the minimum number of states in a non-deterministic finite automation that accepts $$L$$?

Consider the languages $$$\eqalign{ & {L_1} = \left\{ {{0^i}{1^j}\,\left| {i \ne j} \right.} \right\},\,{L_2} = \left\{ {{0^i}{1^j}\,\left| {i = j} \right.} \right\}, \cr & {L_3} = \left\{ {{0^i}{1^j}\,\left| {i = 2j + 1} \right.} \right\}, \cr & {L_4} = \left\{ {{0^i}{1^j}\,\left| {i \ne 2j} \right.} \right\}, \cr} $$$