eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-19
61:1
61:14
10.4230/LIPIcs.MFCS.2016.61
article
On the Complexity of Universality for Partially Ordered NFAs
Krötzsch, Markus
Masopust, Tomás
Thomazo, Michaël
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol058-mfcs2016/LIPIcs.MFCS.2016.61/LIPIcs.MFCS.2016.61.pdf
automata
nondeterminism
partial order
universality