On the complexity of the clone membership problem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00543608" target="_blank" >RIV/67985840:_____/21:00543608 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00224-020-10016-7" target="_blank" >https://doi.org/10.1007/s00224-020-10016-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00224-020-10016-7" target="_blank" >10.1007/s00224-020-10016-7</a>
Alternative languages
Result language
angličtina
Original language name
On the complexity of the clone membership problem
Original language description
We investigate the complexity of the Boolean clone membership problem (CMP): given a set of Boolean functions F and a Boolean function f, determine if f is in the clone generated by F, i.e., if it can be expressed by a circuit with F-gates. Here, f and elements of F are given as circuits or formulas over the usual De Morgan basis. Böhler and Schnoor proved that for any fixed F, the problem is coNP-complete, with a few exceptions where it is in P. Vollmer incorrectly claimed that the full problem CMP is also coNP-complete. We prove that CMP is in fact Theta^P_2-complete, and we complement Böhler and Schnoor's results by showing that for fixed f, the problem is NP-complete unless f is a projection. More generally, we study the problem B-CMP where F and f are given by circuits using gates from B. For most choices of B, we classify the complexity of B-CMP as being Theta^P_2-complete (possibly under randomized reductions), coDP-complete, or in P.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-05497S" target="_blank" >GA19-05497S: Complexity of mathematical proofs and structures</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Theory of Computing Systems
ISSN
1432-4350
e-ISSN
1433-0490
Volume of the periodical
65
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
30
Pages from-to
839-868
UT code for WoS article
000609082600001
EID of the result in the Scopus database
2-s2.0-85099561890