On the length of homing sequences for nondeterministic finite state machines

Authors:
Natalia Kushik;Nina Yevtushenko
Affiliations:
Tomsk State University, Tomsk, Russia,Telecom SudParis, Evry, France;Tomsk State University, Tomsk, Russia
Venue:
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
Year:
2013

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Abstract

Given a reduced deterministic finite state machine, there always exists a homing sequence of length polynomial with respect to the number of states of the machine. For nondeterministic reduced finite state machines, a homing sequence may not exist, and moreover, if it exists, its length can be exponential. We show that the problem of deriving a homing sequence cannot be reduced to deriving a synchronizing word for underlying automata and should be studied independently. We also propose a novel class of (n−1)-input finite state machines with n states whose shortest homing sequence is of length 2n−1−1.