CC-CIRCUITS AND THE EXPRESSIVE POWER OF NILPOTENT ALGEBRAS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452374" target="_blank" >RIV/00216208:11320/22:10452374 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CWR6wMno4p" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CWR6wMno4p</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.46298/LMCS-18(2:12)2022" target="_blank" >10.46298/LMCS-18(2:12)2022</a>
Alternative languages
Result language
angličtina
Original language name
CC-CIRCUITS AND THE EXPRESSIVE POWER OF NILPOTENT ALGEBRAS
Original language description
We show that CC-circuits of bounded depth have the same expressive power as circuits over finite nilpotent algebras from congruence modular varieties. We use this result to phrase a new algebraic version of Barrington, Straubing and Therien's conjecture, which states that CC-circuits of bounded depth need exponential size to compute AND. Furthermore we investigate the complexity of deciding identities and solving equations in a fixed nilpotent algebra. Under the assumption that the conjecture is true, we obtain quasipolynomial algorithms for both problems. On the other hand, if AND is computable by uniform CC-circuits of bounded depth and polynomial size, we can construct a nilpotent algebra in which checking identities is coNP-complete, and solving equations is NP-complete.
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
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Logical Methods in Computer Science
ISSN
1860-5974
e-ISSN
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Volume of the periodical
18
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
15
Pages from-to
12
UT code for WoS article
000806421400001
EID of the result in the Scopus database
2-s2.0-85133200075