Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Hastad, Johan"'
A linearly ordered (LO) $k$-colouring of a hypergraph assigns to each vertex a colour from the set $\{0,1,\ldots,k-1\}$ in such a way that each hyperedge has a unique maximum element. Barto, Batistelli, and Berg conjectured that it is NP-hard to find
Externí odkaz:
http://arxiv.org/abs/2404.19556
Autor:
Håstad, Johan
We study Frege proofs for the one-to-one graph Pigeon Hole Principle defined on the $n\times n$ grid where $n$ is odd. We are interested in the case where each formula in the proof is a depth $d$ formula in the basis given by $\land$, $\lor$, and $\n
Externí odkaz:
http://arxiv.org/abs/2401.15683
Autor:
Håstad, Johan, Risse, Kilian
We study Frege proofs using depth-$d$ Boolean formulas for the Tseitin contradiction on $n \times n$ grids. We prove that if each line in the proof is of size $M$ then the number of lines is exponential in $n/(\log M)^{O(d)}$. This strengthens a rece
Externí odkaz:
http://arxiv.org/abs/2209.05839
Autor:
Guruswami, Venkatesan, Håstad, Johan
We give an explicit construction of length-$n$ binary codes capable of correcting the deletion of two bits that have size $2^n/n^{4+o(1)}$. This matches up to lower order terms the existential result, based on an inefficient greedy choice of codeword
Externí odkaz:
http://arxiv.org/abs/2007.10592
The Galvin problem asks for the minimum size of a family $\mathcal{F} \subseteq \binom{[n]}{n/2}$ with the property that, for any set $A$ of size $\frac n 2$, there is a set $S \in \mathcal{F}$ which is balanced on $A$, meaning that $|S \cap A| = |S
Externí odkaz:
http://arxiv.org/abs/1901.02652
Autor:
Ekerå, Martin, Håstad, Johan
Publikováno v:
In: PQCrypto 2017, Springer LNCS 10346, 347-363 (2017)
In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Eker{\aa} so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one hand, and the
Externí odkaz:
http://arxiv.org/abs/1702.00249
We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed $k \ge 2$, we construct a family of codes over alphabet of size $k$ with positive rate, which allow efficient recovery from a worst-case deletion fraction appro
Externí odkaz:
http://arxiv.org/abs/1507.01719
Publikováno v:
SIAM Journal of Computing, 46(1):132-159, 2017
We prove improved inapproximability results for hypergraph coloring using the low-degree polynomial code (aka, the 'short code' of Barak et. al. [FOCS 2012]) and the techniques proposed by Dinur and Guruswami [FOCS 2013] to incorporate this code for
Externí odkaz:
http://arxiv.org/abs/1311.7407
We study the class of languages, denoted by $\MIP[k, 1-\epsilon, s]$, which have $k$-prover games where each prover just sends a \emph{single} bit, with completeness $1-\epsilon$ and soundness error $s$. For the case that $k=1$ (i.e., for the case of
Externí odkaz:
http://arxiv.org/abs/1301.2729
Autor:
Austrin, Per, Håstad, Johan
Motivated by the pervasiveness of strong inapproximability results for Max-CSPs, we introduce a relaxed notion of an approximate solution of a Max-CSP. In this relaxed version, loosely speaking, the algorithm is allowed to replace the constraints of
Externí odkaz:
http://arxiv.org/abs/1204.5662