Complexity of problems concerning carefully synchronizing words for PFA and directing words for NFA

Authors:
P. V. Martyugin
Affiliations:
Ural State University, Ekaterinburg, Russia
Venue:
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Year:
2010

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Abstract

We show that the problem of checking careful synchronizability of partial finite automata and the problem of finding the shortest carefully synchronizing word are PSPACE-complete. We show that the problem of checking D1, D2 and D3-directability of nondeterministic finite automata and the problem of finding the shortest D1, D2 and D3-directing word are PSPACE-complete. The restrictions of these problems to 2-letter automata remain PSPACE-complete.