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

• Published in: Information processing letters Vol. 112; no. 7; pp. 298 - 301
• Main Authors: Hwang, Iksoon, Yevtushenko, Nina, Cavalli, Ana
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 31.03.2012; Elsevier Sequoia S.A; Elsevier
• Subjects: Computer Science; Distinguishing sequence; Information processing; Networking and Internet Architecture; Non-observable machine; Nondeterministic finite-state machine; Optimization algorithms; Polynomials; Software engineering; Studies; Distinguishing sequence; Nondeterministic finite-state machine; Software engineering; Non-observable machine
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2011.12.012

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. ► 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.