Complexity of infimal observable superlanguages

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00484221" target="_blank" >RIV/67985840:_____/18:00484221 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1109/TAC.2017.2720424" target="_blank" >http://dx.doi.org/10.1109/TAC.2017.2720424</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TAC.2017.2720424" target="_blank" >10.1109/TAC.2017.2720424</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Complexity of infimal observable superlanguages

Popis výsledku v původním jazyce

The infimal prefix-closed, controllable, and observable superlanguage plays an essential role in the relationship between controllability, observability, and co-observability -- the central notions of supervisory control. Existing algorithms are exponential and it is not known whether a polynomial algorithm exists. We answer the question by studying the state complexity of this language. State complexity of a language is the number of states of its minimal deterministic finite automaton (DFA). For a language with state complexity n, we show that the upper bound state complexity on the infimal prefix-closed and observable superlanguage is 2^{n}+1 and that this bound is asymptotically tight. Hence, there is no algorithm computing a DFA of the infimal prefix-closed and observable superlanguage in polynomial time. Our construction shows that such a DFA can be computed in time O(2^n).

Název v anglickém jazyce

Complexity of infimal observable superlanguages

Popis výsledku anglicky

The infimal prefix-closed, controllable, and observable superlanguage plays an essential role in the relationship between controllability, observability, and co-observability -- the central notions of supervisory control. Existing algorithms are exponential and it is not known whether a polynomial algorithm exists. We answer the question by studying the state complexity of this language. State complexity of a language is the number of states of its minimal deterministic finite automaton (DFA). For a language with state complexity n, we show that the upper bound state complexity on the infimal prefix-closed and observable superlanguage is 2^{n}+1 and that this bound is asymptotically tight. Hence, there is no algorithm computing a DFA of the infimal prefix-closed and observable superlanguage in polynomial time. Our construction shows that such a DFA can be computed in time O(2^n).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

IEEE Transactions on Automatic Control

ISSN

0018-9286

e-ISSN

—

Svazek periodika

63

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

6

Strana od-do

249-254

Kód UT WoS článku

000419089000022

EID výsledku v databázi Scopus

2-s2.0-85023760473