On the Complexity of Universality for Partially Ordered NFAs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00462042" target="_blank" >RIV/67985840:_____/16:00462042 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2016.61" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.MFCS.2016.61</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2016.61" target="_blank" >10.4230/LIPIcs.MFCS.2016.61</a>

Result language
angličtina
Original language name
On the Complexity of Universality for Partially Ordered NFAs
Original language description
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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
ISBN
978-3-95977-016-3
ISSN
1868-8969
e-ISSN
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Number of pages
14
Pages from-to
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Publisher name
Schloss Dagstuhl, Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl
Event location
Krakow
Event date
Aug 22, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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