Complexity of universality and related problems for partially ordered NFAs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00476953" target="_blank" >RIV/67985840:_____/17:00476953 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.ic.2017.06.004" target="_blank" >http://dx.doi.org/10.1016/j.ic.2017.06.004</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ic.2017.06.004" target="_blank" >10.1016/j.ic.2017.06.004</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Complexity of universality and related problems for partially ordered NFAs

Popis výsledku v původním jazyce

Partially ordered NFAs (poNFAs) are NFAs where cycles occur only in the form of self-loops. A poNFA is universal if it accepts all words over its alphabet. Deciding universality is PSpace-complete for poNFAs. We show that this remains true when restricting to fixed alphabets. This is nontrivial since standard encodings of symbols in, e.g., binary can turn self-loops into longer cycles. A lower coNP-complete complexity bound is obtained if all self-loops in the poNFA are deterministic. We find that such restricted poNFAs (rpoNFAs) characterize R-trivial languages, and establish the complexity of deciding if the language of an NFA is R-trivial. The limitation to fixed alphabets is essential even in the restricted case: deciding universality of rpoNFAs with unbounded alphabets is PSpace-complete. Consequently, we obtain the complexity results for inclusion and equivalence problems. Finally, we show that the languages of rpoNFAs are definable by deterministic regular expressions.

Název v anglickém jazyce

Complexity of universality and related problems for partially ordered NFAs

Popis výsledku anglicky

Partially ordered NFAs (poNFAs) are NFAs where cycles occur only in the form of self-loops. A poNFA is universal if it accepts all words over its alphabet. Deciding universality is PSpace-complete for poNFAs. We show that this remains true when restricting to fixed alphabets. This is nontrivial since standard encodings of symbols in, e.g., binary can turn self-loops into longer cycles. A lower coNP-complete complexity bound is obtained if all self-loops in the poNFA are deterministic. We find that such restricted poNFAs (rpoNFAs) characterize R-trivial languages, and establish the complexity of deciding if the language of an NFA is R-trivial. The limitation to fixed alphabets is essential even in the restricted case: deciding universality of rpoNFAs with unbounded alphabets is PSpace-complete. Consequently, we obtain the complexity results for inclusion and equivalence problems. Finally, we show that the languages of rpoNFAs are definable by deterministic regular expressions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Information and Computation

ISSN

0890-5401

e-ISSN

—

Svazek periodika

255

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

177-192

Kód UT WoS článku

000407658600009

EID výsledku v databázi Scopus

2-s2.0-85022196483