Complexity of infimal observable superlanguages
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Complexity of infimal observable superlanguages
Original language description
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).
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20205 - Automation and control systems
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Automatic Control
ISSN
0018-9286
e-ISSN
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Volume of the periodical
63
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
6
Pages from-to
249-254
UT code for WoS article
000419089000022
EID of the result in the Scopus database
2-s2.0-85023760473