Related papers: The Satisfiability Threshold for k-XORSAT
We study a random system of cn linear equations over n variables in GF(2), where each equation contains exactly r variables; this is equivalent to r-XORSAT. Previous work has established a clustering threshold, c^*_r for this model: if…
Quantum satisfiability is a constraint satisfaction problem that generalizes classical boolean satisfiability. In the quantum k-SAT problem, each constraint is specified by a k-local projector and is satisfied by any state in its nullspace.…
Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying…
We prove that a random 3-SAT instance with clause-to-variable density less than 3.52 is satisfiable with high probability. The proof comes through an algorithm which selects (and sets) a variable depending on its degree and that of its…
In this paper we study a variation of the random $k$-SAT problem, called polarized random $k$-SAT. In this model there is a polarization parameter $p$, and in half of the clauses each variable occurs negated with probability $p$ and pure…
The random $k$-SAT problem serves as a model that represents the 'typical' $k$-SAT instances. This model is thought to undergo a phase transition as the clause density changes, and it is believed that the random $k$-SAT problem is primarily…
Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and…
The Random K-Satisfiability Problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M=alpha N random logical clauses containing K variables each, is studied using the replica symmetric…
We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two random combinatorial problems: k-XORSAT and k-SAT. We present a general method for establishing the stability of these solutions with respect to further steps of…
We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model of random k-SAT exhibits a sharp threshold for…
Since the early 2000s physicists have developed an ingenious but non-rigorous formalism called the cavity method to put forward precise conjectures on phase transitions in random problems [Mezard, Parisi, Zecchina: Science 2002]. The cavity…
We present efficient counting and sampling algorithms for random $k$-SAT when the clause density satisfies $\alpha \le \frac{2^k}{\mathrm{poly}(k)}.$ In particular, the exponential term $2^k$ matches the satisfiability threshold…
Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be…
We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp…
The random 3-satisfiability (3-SAT) problem is in the unsatisfiable (UNSAT) phase when the clause density $\alpha$ exceeds a critical value $\alpha_s \approx 4.267$. However, rigorously proving the unsatisfiability of a given large 3-SAT…
Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…
The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k>=3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
The Random Satisfiability problem has been intensively studied for decades. For a number of reasons the focus of this study has mostly been on the model, in which instances are sampled uniformly at random from a set of formulas satisfying…
We show that Not-All-Equal 3-Sat remains NP-complete when restricted to instances that simultaneously satisfy the following properties: (i) The clauses are given as the disjoint union of k partitions, for any fixed $k \geq 4$, of the…