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Directable nondeterministic automata
B. Imreh 3, M. Steinby 4
Dedicated to Professor Ferenc Gécseg on the occasion of his 60th birthday
Abstract
An automaton is directable if it has a directing word which takes it from every state to the same state. For nondeterministic (n.d.) automata directability can be defined in several meaningful ways. We consider three such notions. An input word w of an n.d. automaton A is
(1) D1-directing if the set of states aw in which A may be after reading w consists of the same single state c for all initial states a;
(2) D2-directing if the set aw is independent of the initial state a;
(3) D3-directing if some state c appears in all of the sets aw.
We consider the sets of D1-, D2- and D3-directing words of a given n.d. automaton, and compare the classes of D1-, D2- and D3-directable n.d. automata with each other. We also estimate the lengths of the longest possible minimum-length D1-, D2- and D3-directing words of an n-state n.d. automaton. All questions are studied separately for n.d. automata which have at least one next state for every input-state pair.
Footnotes:
1 This work has been supported by the Hungarian National Foundation for Scientific Research, Grant T014888, the Hungarian-Finnish S - T Co-operation Programme for 1997-1999, Grant SF-10/97 and the Ministry of Culture and Education of Hungary, Grant PFP-4123/1997.
2 This work has been supported by the Hungarian National Foundation for Scientific Research, Grant T014888, the Hungarian-Finnish S - T Co-operation Programme for 1997-1999, Grant SF-10/97 and the Ministry of Culture and Education of Hungary, Grant PFP-4123/1997.
3 Institute of Informatics, József Attila University, Árpád tér 2, H-6720 Szeged, Hungary
4 TUCS and Department of Mathematics, University of Turku, FIN-20014 Turku, Finland