On the Complexity of Universality for Partially Ordered NFAs - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2016

On the Complexity of Universality for Partially Ordered NFAs

Résumé

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.
Fichier principal
Vignette du fichier
mfcs2016-mktmmt.pdf (541 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01334958 , version 1 (21-06-2016)

Licence

Paternité

Identifiants

Citer

Markus Krötzsch, Tomáš Masopust, Michaël Thomazo. On the Complexity of Universality for Partially Ordered NFAs . 41st International Symposium on Mathematical Foundations of Computer Science , Aug 2016, Krakow, Poland. ⟨10.4230/LIPIcs.MFCS.2016.62⟩. ⟨hal-01334958⟩
701 Consultations
62 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More