Related papers: Biased random k-SAT
Majority-SAT is the problem of determining whether an input $n$-variable formula in conjunctive normal form (CNF) has at least $2^{n-1}$ satisfying assignments. Majority-SAT and related problems have been studied extensively in various AI…
In a broad class of sparse random constraint satisfaction problems(CSP), deep heuristics from statistical physics predict that there is a condensation phase transition before the satisfiability threshold, governed by one-step replica…
In the last decades, many efforts have focused on analyzing typical-case hardness in optimization and inference problems. Some recent work has pointed out that polynomial algorithms exist, running with a time that grows more than linearly…
We introduce a new model for the generation of random satisfiability problems. It is an extension of the hyper-SAT model of Ricci-Tersenghi, Weigt and Zecchina, which is a variant of the famous K-SAT model: it is extended to q-state…
How many $k$-SAT functions on $n$ boolean variables are there? What does a typical such function look like? Bollob\'as, Brightwell, and Leader conjectured that, for each fixed $k \ge 2$, the number of $k$-SAT functions on $n$ variables is…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…
For each integer $n$ we present an explicit formulation of a compact linear program, with $O(n^3)$ variables and constraints, which determines the satisfiability of any 2SAT formula with $n$ boolean variables by a single linear…
The natural generalization of the Boolean satisfiability problem to optimization problems is the task of determining the maximum number of clauses that can simultaneously be satisfied in a propositional formula in conjunctive normal form.…
In this paper we detail a classical algorithmic approach to the k-satisfiability (k-SAT) problem that is inspired by the quantum amplitude amplification algorithm. This work falls under the emerging field of quantum-inspired classical…
The random K-satisfiability (K-SAT) problem is an important problem for studying typical-case complexity of NP-complete combinatorial satisfaction; it is also a representative model of finite-connectivity spin-glasses. In this paper we…
We study the geometric structure of the set of solutions of random $\epsilon$-1-in-k SAT problem. For $l\geq 1$, two satisfying assignments $A$ and $B$ are $l$-connected if there exists a sequence of satisfying assignments connecting them…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
The problem 2-Xor-Sat asks for the probability that a random expression, built as a conjunction of clauses $x \oplus y$, is satisfiable. We revisit this classical problem by giving an alternative, explicit expression of this probability. We…
We consider random systems of equations x_1 + ... + x_k = a; 0 <= a <= 2 which are interpreted as equations modulo 3: We show for k >= 15 that the satisfiability threshold of such systems occurs where the 2-core has density 1: We show a…
We study the random K-satisfiability problem using a partition function where each solution is reweighted according to the number of variables that satisfy every clause. We apply belief propagation and the related cavity method to the…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
Constraint Satisfaction Problems are ubiquitous in fields ranging from the physics of solids to artificial intelligence. In many cases, such systems undergo a transition when the ratio of constraints to variables reaches some value…
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
Stochastic Boolean Satisfiability (SSAT) is a logical formalism to model decision problems with uncertainty, such as Partially Observable Markov Decision Process (POMDP) for verification of probabilistic systems. SSAT, however, is limited…