Abstract
An automaton is partially ordered if the only cycles in its transition diagram are self-loops. We study the universality problem for ptNFAs, a class of partially ordered NFAs recognizing piecewise testable languages. The universality problem asks if an automaton accepts all words over its alphabet. Deciding universality for both NFAs and partially ordered NFAs is PSpace-complete. For ptNFAs, the complexity drops to coNP-complete if the alphabet is fixed but is open if the alphabet may grow. We show, using a novel and nontrivial construction, that the problem is PSpace-complete if the alphabet may grow polynomially.
Supported by DFG grants KR 4381/1-1 & CRC 912 (HAEC), and by RVO 67985840.
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Masopust, T., Krötzsch, M. (2018). Deciding Universality of ptNFAs is PSpace-Complete. In: Tjoa, A., Bellatreche, L., Biffl, S., van Leeuwen, J., Wiedermann, J. (eds) SOFSEM 2018: Theory and Practice of Computer Science. SOFSEM 2018. Lecture Notes in Computer Science(), vol 10706. Edizioni della Normale, Cham. https://doi.org/10.1007/978-3-319-73117-9_29
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