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Electronic Colloquium on Computational Complexity

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Reports tagged with representations of the symmetric group:
TR94-014 | 12th December 1994
Miklos Ajtai

The Independence of the modulo p Counting Principles

The modulo $p$ counting principle is a first-order axiom
schema saying that it is possible to count modulo $p$ the number of
elements of the first-order definable subsets of the universe (and of
the finite Cartesian products of the universe with itself) in a
consistent way. It trivially holds on ... more >>>

TR94-015 | 12th December 1994
Miklos Ajtai

Symmetric Systems of Linear Equations modulo $p$

Suppose that $p$ is a prime number $A$ is a finite set
with $n$ elements
and for each sequence $a=<a_{1},...,a_{k}>$ of length $k$ from the
elements of
$A$, $x_{a}$ is a variable. (We may think that $k$ and $p$ are fixed an
$n$ is sufficiently large.) We will ... more >>>

TR16-162 | 18th October 2016
Joshua Grochow

NP-hard sets are not sparse unless P=NP: An exposition of a simple proof of Mahaney's Theorem, with applications

Mahaney's Theorem states that, assuming P $\neq$ NP, no NP-hard set can have a polynomially bounded number of yes-instances at each input length. We give an exposition of a very simple unpublished proof of Manindra Agrawal whose ideas appear in Agrawal-Arvind ("Geometric sets of low information content," Theoret. Comp. Sci., ... more >>>

ISSN 1433-8092 | Imprint