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

Authors:
Iksoon Hwang;Nina Yevtushenko;Ana Cavalli
Affiliations:
Software-Networks Department, Telecom SudParis, 9 rue Charles Fourier, 91011 Evry Cedex, France;Department of EECS, Tomsk State University, 36 Lenin Street, Tomsk, 634050, Russia;Software-Networks Department, Telecom SudParis, 9 rue Charles Fourier, 91011 Evry Cedex, France
Venue:
Information Processing Letters
Year:
2012

Citing 2
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Abstract

In this paper we show that the upper bound 2^n-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 2^n-3 but can be distinguished by an input sequence of length 2^n-2.