A low complexity probabilistic test for integer multiplication
- Grigoriev, Dima
- Tenenbaum, Gérald
DOIAbstract
AbstractA probabilistic test for equality a=bc for given n-bit integers a,b,c is designed within complexity n(loglogn)exp{O(log∗n)}
AbstractA probabilistic test for equality a=bc for given n-bit integers a,b,c is designed within complexity n(loglogn)exp{O(log∗n)}
We ask for feasibly constructive proofs of known circuit lower bounds for explicit functions on bit ...
AbstractFor logylog log x → ∞ as x → ∞, ψ(Cx, y) ≈ Cψ(x, y) uniformly for C in compact subsets of (0...
Abstract. An algorithm is presented that probabilistically computes the exact inverse of a nonsingul...
AbstractA probabilistic test for equality a=bc for given n-bit integers a,b,c is designed within com...
Let M(n) denote the bit complexity of multiplying n-bit integers, let ω ∈ (2, 3] be an exponent for ...
We give a new proof of Fürer's bound for the cost of multiplying n-bit integers in the bit complexit...
Define $||n||$ to be the \emph{complexity} of $n$, which is the smallest number of $1$s needed to wr...
AbstractWe prove an exponential lower bound 2Ω(n/logn) on the size of any randomized ordered read-on...
A heuristic analysis is presented of the complexity of an algorithm which was applied recently to ve...
AbstractWe analyse two recent probabilistic primality testing algorithms; the first one is derived f...
AbstractA Σ32 Boolean circuit has 3 levels of gates. The input level is comprised of OR gates each t...
The \textit{integer complexity} of a positive integer $n$, denoted $f(n)$, is defined as the least n...
The combined universal probability m(D) of strings x in sets D is close to max \m(x) over x in D: th...
© 2020 ACM. We establish several "sharp threshold" results for computational complexity. For certain...
AbstractA probabilistic algorithm for testing primality of a large integer ‘n’ is introduced. The al...
We ask for feasibly constructive proofs of known circuit lower bounds for explicit functions on bit ...
AbstractFor logylog log x → ∞ as x → ∞, ψ(Cx, y) ≈ Cψ(x, y) uniformly for C in compact subsets of (0...
Abstract. An algorithm is presented that probabilistically computes the exact inverse of a nonsingul...
AbstractA probabilistic test for equality a=bc for given n-bit integers a,b,c is designed within com...
Let M(n) denote the bit complexity of multiplying n-bit integers, let ω ∈ (2, 3] be an exponent for ...
We give a new proof of Fürer's bound for the cost of multiplying n-bit integers in the bit complexit...
Define $||n||$ to be the \emph{complexity} of $n$, which is the smallest number of $1$s needed to wr...
AbstractWe prove an exponential lower bound 2Ω(n/logn) on the size of any randomized ordered read-on...
A heuristic analysis is presented of the complexity of an algorithm which was applied recently to ve...
AbstractWe analyse two recent probabilistic primality testing algorithms; the first one is derived f...
AbstractA Σ32 Boolean circuit has 3 levels of gates. The input level is comprised of OR gates each t...
The \textit{integer complexity} of a positive integer $n$, denoted $f(n)$, is defined as the least n...
The combined universal probability m(D) of strings x in sets D is close to max \m(x) over x in D: th...
© 2020 ACM. We establish several "sharp threshold" results for computational complexity. For certain...
AbstractA probabilistic algorithm for testing primality of a large integer ‘n’ is introduced. The al...
We ask for feasibly constructive proofs of known circuit lower bounds for explicit functions on bit ...
AbstractFor logylog log x → ∞ as x → ∞, ψ(Cx, y) ≈ Cψ(x, y) uniformly for C in compact subsets of (0...
Abstract. An algorithm is presented that probabilistically computes the exact inverse of a nonsingul...
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