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Theorem in computational complexity theory
Mahaney's theorem is a theorem in computational complexity theory proven by Stephen Mahaney that states that If any sparse language is NP-hard, then P=NP
Mahaney's_theorem
then P = NP. (Mahaney, 1982) used this to prove Mahaney's theorem that if any sparse language is NP-complete, then P = NP. Mahaney's argument does not
Sparse_language
Complexity class
co-NP-complete (or even just co-NP-hard), then P = NP. This result is used in Mahaney's theorem. Arora, Sanjeev; Barak, Boaz (2009). Complexity Theory: A Modern Approach
Co-NP-complete
Set of problems solved by small circuits
9781611977936.15 Jin-Yi Cai. Lecture 11: P/poly, Sparse Sets, and Mahaney's Theorem. CS 810: Introduction to Complexity Theory. The University of Wisconsin–Madison
P/poly
American computer scientist (1928–2022)
of research on the structure of NP-complete sets, culminating in Mahaney's theorem on the nonexistence of sparse NP-complete sets. He and his coauthors
Juris_Hartmanis
NP/poly is used in a variation of Mahaney's theorem on the non-existence of sparse NP-complete languages. Mahaney's theorem itself states that the number
NP/poly
Unsolved problem in structural complexity theory
reductions) is in fact equivalent to the statement that P ≠ NP; this is Mahaney's theorem. Even for a relaxed definition of NP-completeness using Turing reductions
Berman–Hartmanis_conjecture
Formal language in computational complexity theory
[1] Lance Fortnow. Favorite Theorems: Small Sets. April 18, 2006. http://weblog.fortnow.com/2006/04/favorite-theorems-small-sets.html Complexity Zoo:
Unary_language
MAHANEYS THEOREM
MAHANEYS THEOREM
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Indian, Tamil
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Hindu, Indian, Marathi, Oriya, Sanskrit, Telugu
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Tamil
One who save the world
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Gujarati, Hindu, Indian
Lord Shiva
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Biblical
A comforter.
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Hindu, Indian, Malayalam, Marathi, Tamil
Goddess Lakshmi
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Australian, Irish
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Hindu
Worthy of honor
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Great god.
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Hindu, Indian
Great Strength; Lord of Shiva
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Hindu
One who save the world
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Indian
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Tamil
Mahaniya | மஹாநியாÂ
Worthy of honor
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MAHANEYS THEOREM
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Hair
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Surname or Lastname
English
English : variant spelling of Hawk.
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Indian, Sanskrit
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Muslim
Surname or Lastname
English
English : habitational name from a place in Norfolk, so called from the Old Norse personal name Fili or Fila (of uncertain origin) + Old Norse býr ‘farm’, ‘settlement’.
Boy/Male
Danish, Finnish, German
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Great; Purity; Foremost; Best
MAHANEYS THEOREM
MAHANEYS THEOREM
MAHANEYS THEOREM
MAHANEYS THEOREM
MAHANEYS THEOREM
a.
Theorematic.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
v. t.
To formulate into a theorem.
n.
A numerical coefficient in any particular case of the binomial theorem.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.
n.
That which is considered and established as a principle; hence, sometimes, a rule.
a.
Alt. of Theorematical
n.
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.
n.
A statement of a principle to be demonstrated.
n.
A theorem or proposition so easy of demonstration as to be almost self-evident.
n.
One who constructs theorems.