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

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⩾2n⩾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.

► We study the distinguishability of sets of states of non-observable NFSMs. ► We examine the length of input sequences that distinguish two sets of states. ► The bound 2n − 2 on the length of such sequences is tight for an NFSM with n states. ► We show that the bound 2n − 2 is also tight for an NFSM of polynomial size.