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Electronic Colloquium on Computational Complexity

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Reports tagged with finite structures:
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 >>>

TR11-102 | 31st July 2011
Miklos Ajtai

Determinism Versus Nondeterminism with Arithmetic Tests and Computation

Revisions: 1

For each natural number $d$ we consider a finite structure $M_{d}$ whose
universe is the set of all $0,1$-sequence of length $n=2^{d}$, each
representing a natural number in the set $\lbrace 0,1,...,2^{n}-1\rbrace
$ in binary form.
The operations included in the structure are the
constants $0,1,2^{n}-1,n$, multiplication and addition ... more >>>

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