On the Complexity of Universality for Partially Ordered NFAs

0462042 - MÚ 2017 RIV DE eng C - Conference Paper (international conference)
Krötzsch, M. - Masopust, Tomáš - Thomazo, M.
On the Complexity of Universality for Partially Ordered NFAs.
41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Dagstuhl: Schloss Dagstuhl, Leibniz-Zentrum fuer Informatik, 2016 - (Faliszewski, P.; Muscholl, A.; Niedermeier, R.), 61:1-61:14. Leibniz International Proceedings in Informatics (LIPIcs), 58. ISBN 978-3-95977-016-3. ISSN 1868-8969.
[41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Krakow (PL), 22.08.2016-26.08.2016]
Institutional support: RVO:67985840
Keywords : automata * nondeterminism * partial order * universality
Subject RIV: BA - General Mathematics
http://drops.dagstuhl.de/opus/volltexte/2016/6473/

Partially ordered nondeterminsitic finite automata (poNFAs) are NFAs whose transition relation induces a partial order on states, i.e., for which cycles occur only in the form of self-loops on a single state. A poNFA is universal if it accepts all words over its input alphabet. Deciding universality is PSpace-complete for poNFAs, and we show that this remains true even when restricting to a fixed alphabet. This is nontrivial since standard encodings of alphabet symbols in, e.g., binary can turn self-loops into longer cycles. A lower coNP-complete complexity bound can be obtained if we require that all self-loops in the poNFA are deterministic, in the sense that the symbol read in the loop cannot occur in any other transition from that state. We find that such restricted poNFAs (rpoNFAs) characterise the class of R-trivial languages, and we establish the complexity of deciding if the language of an NFA is R-trivial. Nevertheless, the limitation to fixed alphabets turns out to be essential even in the restricted case: deciding universality of rpoNFAs with unbounded alphabets is PSPACE-complete. Our results also prove the complexity of the inclusion and equivalence problems, since universality provides the lower bound, while the upper bound is mostly known or proved in the paper.
Permanent Link: http://hdl.handle.net/11104/0261588