Related papers: On the Regularity of Random 2-SAT and 3-SAT

We consider "unconstrained" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-homogeneous equations in $\mathbb{F}_2$ over $n$ variables, each equation containing $k \geq 3$ variables, and also consider a "constrained"…

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…

To study the structure of solutions for random k-SAT and random CSPs, this paper introduces the concept of average similarity degree to characterize how solutions are similar to each other. It is proved that under certain conditions, as r…

We consider the random 2-satisfiability problem, in which each instance is a formula that is the conjunction of m clauses of the form (x or y), chosen uniformly at random from among all 2-clauses on n Boolean variables and their negations.…

Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential…

Regular signed SAT is a variant of the well-known satisfiability problem in which the variables can take values in a fixed set V \subset [0,1], and the `literals' have the form "x \le a" or "x \ge a". We answer some open question regarding…

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 QSAT problem is the quantified version of the SAT problem. We show the existence of a threshold effect for the phase transition associated with the satisfiability of random quantified extended 2-CNF formulas. We consider boolean CNF…

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of F with high probability for constraint densities m/n<(1-eps_k)2^k\ln(k)/k,…

We consider "unconstrained" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-homogeneous equations in $\mathbb{F}_2$ over $n$ variables, each equation containing $k \ge 3$ variables, and also consider a "constrained"…

We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_*(k)$ such that a random $k$-SAT formula of clause density $\alpha$ is with…

Using the cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to…

The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…

It is well known that, as $n$ tends to infinity, the probability of satisfiability for a random 2-SAT formula on $n$ variables, where each clause occurs independently with probability $\alpha/2n$, exhibits a sharp threshold at $\alpha=1$.…

Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…

In signed k-SAT problems, one fixes a set M and a set $\mathcal S$ of subsets of M, and is given a formula consisting of a disjunction of m clauses, each of which is a conjunction of k literals. Each literal is of the form "$x \in S$",…

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…

We give a nearly linear-time algorithm to approximately sample satisfying assignments in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previously known sampling algorithm for the random…

We consider constraint satisfaction problems parameterized above or below tight bounds. One example is MaxSat parameterized above $m/2$: given a CNF formula $F$ with $m$ clauses, decide whether there is a truth assignment that satisfies at…

Depth-3 circuit lower bounds and $k$-SAT algorithms are intimately related; the state-of-the-art $\Sigma^k_3$-circuit lower bound and the $k$-SAT algorithm are based on the same combinatorial theorem. In this paper we define a problem which…