• Source: Elementary

Elementary may refer to:




Arts, entertainment, and media






= Music

=
Elementary (Cindy Morgan album), 2001
Elementary (The End album), 2007
Elementary, a Melvin "Wah-Wah Watson" Ragin album, 1977




= Other uses in arts, entertainment, and media

=
Elementary (TV series), a 2012 American drama television series
"Elementary, my dear Watson", a catchphrase of Sherlock Holmes




Education


Elementary and Secondary Education Act, US
Elementary education, or primary education, the first years of formal, structured education
Elementary Education Act 1870, England and Wales
Elementary school, a school providing elementary or primary education




Science and technology


ELEMENTARY, a class of objects in computational complexity theory
Elementary, a widget set based on the Enlightenment Foundation Libraries
Elementary abelian group, an abelian group in which every nontrivial element is of prime order
Elementary algebra
Elementary arithmetic
Elementary charge, e, of a single electron
Elementary definition, in mathematical logic
elementary OS, a Linux distribution
Elementary particle, in particle physics
Elementary proof
Elementary function




See also


Element (disambiguation)
Elemental (disambiguation)
• Source: ELEMENTARY

In computational complexity theory, the complexity class





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{\displaystyle {\mathsf {ELEMENTARY}}}

consists of the decision problems that can be solved in time bounded by an elementary recursive function. The most quickly-growing elementary functions are obtained by iterating an exponential function such as




2

n




{\displaystyle 2^{n}}

for a bounded number



k


{\displaystyle k}

of iterations,











2



2



2



⋅



⋅



⋅


n






















}

k
.


{\displaystyle \left.{\begin{matrix}2^{\scriptstyle 2^{\scriptstyle 2^{\scriptstyle \cdot ^{\scriptstyle \cdot ^{\scriptstyle \cdot ^{\scriptstyle n}}}}}}\end{matrix}}\right\}k.}


Thus,





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{\displaystyle {\mathsf {ELEMENTARY}}}

is the union of the classes










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=

⋃

k
∈

N



k




-


E
X
P








=


D
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I
M
E



(

2

n


)

∪


D
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I
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E



(

2


2

n




)

∪


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E



(

2


2


2

n






)

∪
⋯
.






{\displaystyle {\begin{aligned}{\mathsf {ELEMENTARY}}&=\bigcup _{k\in \mathbb {N} }k{\mathsf {{\mbox{-}}EXP}}\\&={\mathsf {DTIME}}\left(2^{n}\right)\cup {\mathsf {DTIME}}\left(2^{2^{n}}\right)\cup {\mathsf {DTIME}}\left(2^{2^{2^{n}}}\right)\cup \cdots .\end{aligned}}}


It is sometimes described as iterated exponential time, though this term more commonly refers to time bounded by the tetration function.

This complexity class can be characterized by a certain class of "iterated stack automata", pushdown automata that can store the entire state of a lower-order iterated stack automaton in each cell of their stack. These automata can compute every language in





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{\displaystyle {\mathsf {ELEMENTARY}}}

, and cannot compute languages beyond this complexity class. The time hierarchy theorem implies that





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{\displaystyle {\mathsf {ELEMENTARY}}}

has no complete problems.
Every elementary recursive function can be computed in a time bound of this form, and therefore every decision problem whose calculation uses only elementary recursive functions belongs to the complexity class





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{\displaystyle {\mathsf {ELEMENTARY}}}

.




References

Kata Kunci Pencarian:

• Elementary School Musical (South Park)
• Hero Elementary
• Elementary (seri televisi)
• Muatan listrik partikel
• Elementary OS
• Abbott Elementary
• Ilham Akbar Habibie
• Ribut Hari Wibowo
• Elementary School Musical (The Simpsons)
• PlayStation 2
• Elementary
• ELEMENTARY
• Abbott Elementary
• Elementary charge
• Elementary matrix
• Elementary function
• Elementary particle
• Elementary equivalence
• Berryessa Union School District
• List of Abbott Elementary episodes