Related papers: A New Bound for 3-Satisfiable MaxSat and its Algor…
The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. Barto [LICS '19] has shown that a…
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 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…
We model Semantic Self-Verification (SSV) as the problem of determining whether a statement accurately characterizes its own semantic properties within a given interpretive framework that formalizes a challenge in AI safety and fairness:…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
Presentation of a Method for determining whether a problem 3Sat has solution, and if yes to find one, in time max O(n^15). Is thus proved that the problem 3Sat is fully resolved in polynomial time and therefore that it is in P, by the work…
The Local Search algorithm (or Hill Climbing, or Iterative Improvement) is one of the simplest heuristics to solve the Satisfiability and Max-Satisfiability problems. It is a part of many satisfiability and max-satisfiability solvers, where…
Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with…
The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we investigate a descriptor approach based on lattice properties. This paper proposes a new way to…
In this paper, we discussed CNF-SAT problem (NP-Complete problem) and analysis two solutions that can solve the problem, the PL-Resolution algorithm and the WalkSAT algorithm. PL-Resolution is a sound and complete algorithm that can be used…
We study the complexity of the following "resolution width problem": Does a given 3-CNF have a resolution refutation of width k? We prove that the problem cannot be decided in time O(n^((k-3)/12)). This lower bound is unconditional and does…
The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
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…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…
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…
Counterfactual explanations (CFEs) exemplify how to minimally modify a feature vector to achieve a different prediction for an instance. CFEs can enhance informational fairness and trustworthiness, and provide suggestions for users who…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…
We present a deterministic approximation algorithm to compute logarithm of the number of `good' truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by `good' we mean that violate a small fraction of clauses).…