Tight bound on the length of distinguishing sequences for non-observable nondeterministic Finite-State Machines with a polynomial number of inputs and outputs

International audience; In this paper we show that the upper bound 2n - 2 on the length of input sequences that distinguish two sets of states is tight for a non-observable NFSM with n states and a polynomial number of inputs and outputs. For each n>=2, there exists a non-observable NFSM M with n states, a single input symbol, and n output symbols such that there are two sets of states in M which are not distinguishable by each input sequence of length 2n - 3 but can be distinguished by an input sequence of length 2n - 2.