Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with precisely $k$ non-zero entries per row and let $y\in F_q^m$ be a random vector chosen independently of $A$. We identify the threshold $m/n$ up to which the linear system $A x=y$ has a solution with high probability and analyse the geometry of the set of solutions. In the special case $q=2$, known as the random $k$-XORSAT problem, the threshold was determined by [Dubois and Mandler 2002, Dietzfelbinger et al. 2010, Pittel and Sorkin 2016], and the proof technique was subsequently extended to the cases $q=3,4$ [Falke and Goerdt 2012]. But the argument depends on technically demanding second moment calculations that do not generalise to $q>3$. Here we approach the problem ...
Let $\mathbf{A}$ be an $n\times n$-matrix over $\mathbb{F}_2$ whose every entry equals $1$ with prob...
International audienceWe investigate geometrical properties of the random K-satisfiability problem u...
AbstractIt is widely believed that the probability of satisfiability for random k-SAT formulae exhib...
We consider "unconstrained" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-...
Abstract. We consider “unconstrained ” random k-XORSAT, which is a uniformly random system of m line...
AbstractVarious experimental investigations have shown a sharp transition between satisfiability and...
AbstractWe study threshold properties of random constraint satisfaction problems under a probabilist...
AbstractWe investigate geometrical properties of the random K-satisfiability problem using the notio...
AbstractThe sharp Satisfiability threshold is well known for random k-SAT formulas and is due to cer...
Abstract. Many NP-complete constraint satisfaction problems appear to undergo a “phase transition” f...
AbstractWe consider random instances I of a constraint satisfaction problem generalizing k-SAT: give...
Despite much work over the previous decade, the Satisfiability Threshold Conjecture remains open. ...
AbstractThe problem of determining the unsatisfiability threshold for random 3-SAT formulas consists...
For a planted satisfiability problem on n variables with k variables per constraint, the planted ass...
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The ...
Let $\mathbf{A}$ be an $n\times n$-matrix over $\mathbb{F}_2$ whose every entry equals $1$ with prob...
International audienceWe investigate geometrical properties of the random K-satisfiability problem u...
AbstractIt is widely believed that the probability of satisfiability for random k-SAT formulae exhib...
We consider "unconstrained" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-...
Abstract. We consider “unconstrained ” random k-XORSAT, which is a uniformly random system of m line...
AbstractVarious experimental investigations have shown a sharp transition between satisfiability and...
AbstractWe study threshold properties of random constraint satisfaction problems under a probabilist...
AbstractWe investigate geometrical properties of the random K-satisfiability problem using the notio...
AbstractThe sharp Satisfiability threshold is well known for random k-SAT formulas and is due to cer...
Abstract. Many NP-complete constraint satisfaction problems appear to undergo a “phase transition” f...
AbstractWe consider random instances I of a constraint satisfaction problem generalizing k-SAT: give...
Despite much work over the previous decade, the Satisfiability Threshold Conjecture remains open. ...
AbstractThe problem of determining the unsatisfiability threshold for random 3-SAT formulas consists...
For a planted satisfiability problem on n variables with k variables per constraint, the planted ass...
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The ...
Let $\mathbf{A}$ be an $n\times n$-matrix over $\mathbb{F}_2$ whose every entry equals $1$ with prob...
International audienceWe investigate geometrical properties of the random K-satisfiability problem u...
AbstractIt is widely believed that the probability of satisfiability for random k-SAT formulae exhib...