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In this paper I present a 3SAT algorithm based on the randomized algorithm of Papadimitriou from 1991, and Schoning from 1991. We also present strong arguments that this algorithm finds a solution (if it exists) for a 3SAT problem with high…

Data Structures and Algorithms · Computer Science 2018-01-03 Cristian Dumitrescu

Horn-satisfiability or Horn-SAT is the problem of deciding whether a satisfying assignment exists for a Horn formula, a conjunction of clauses each with at most one positive literal (also known as Horn clauses). It is a well-known…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-05-26 Ananth Hari , Uzi Vishkin

Survey propagation is a powerful technique from statistical physics that has been applied to solve the 3-SAT problem both in principle and in practice. We give, using only probability arguments, a common derivation of survey propagation,…

Statistical Mechanics · Physics 2007-05-23 Erik Aurell , Uri Gordon , Scott Kirkpatrick

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…

Data Structures and Algorithms · Computer Science 2011-08-25 G. Gutin , A. Yeo

We prove that throughout the satisfiable phase, the logarithm of the number of satisfying assignments of a random 2-SAT formula satisfies a central limit theorem. This implies that the log of the number of satisfying assignments exhibits…

Discrete Mathematics · Computer Science 2024-09-23 Arnab Chatterjee , Amin Coja-Oghlan , Noela Müller , Connor Riddlesden , Maurice Rolvien , Pavel Zakharov , Haodong Zhu

Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. We study random ensembles of the QMA$_1$-complete…

Quantum Physics · Physics 2010-04-29 C. R. Laumann , R. Moessner , A. Scardicchio , S. L. Sondhi

We develop a new approach to multi-label conformal prediction in which we aim to output a precise set of promising prediction candidates with a bounded number of incorrect answers. Standard conformal prediction provides the ability to adapt…

Machine Learning · Computer Science 2022-02-16 Adam Fisch , Tal Schuster , Tommi Jaakkola , Regina Barzilay

Let $Z(F)$ be the number of solutions of a random $k$-satisfiability formula $F$ with $n$ variables and clause density $\alpha$. Assume that the probability that $F$ is unsatisfiable is $O(1/\log(n)^{1+\e})$ for $\e>0$. We show that…

Discrete Mathematics · Computer Science 2010-06-23 Emmanuel Abbe , Andrea Montanari

In this paper we study biased random K-SAT problems in which each logical variable is negated with probability $p$. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the…

Disordered Systems and Neural Networks · Physics 2009-11-10 A. Ramezanpour , S. Moghimi-Araghi

The problem of identifying a planted assignment given a random $k$-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution becomes unique and can be identified given a formula with $O(n\log…

Computational Complexity · Computer Science 2018-03-07 Vitaly Feldman , Will Perkins , Santosh Vempala

Constrained-random simulation is the predominant approach used in the industry for functional verification of complex digital designs. The effectiveness of this approach depends on two key factors: the quality of constraints used to…

Logic in Computer Science · Computer Science 2014-03-26 Supratik Chakraborty , Kuldeep S. Meel , Moshe Y. Vardi

Quantum k-SAT (the problem of determining whether a k-local Hamiltonian is frustration-free) is known to be QMA_1-complete for k >= 3, and hence likely hard for quantum computers to solve. Building on a classical result of Alon and Shapira,…

Quantum Physics · Physics 2025-09-03 Ashley Montanaro , Changpeng Shao , Dominic Verdon

The Boolean Satisfiability Problem is perhaps one of the most well-known problems in theoretical computer science. On the one hand, it is proven to be NP-complete, which means that it is generally considered hard to solve. On the other…

Logic in Computer Science · Computer Science 2026-03-03 Flora Rädiker

The following paper proposes a new approach to determine whether a logical (CNF) formula is satisfiable or not using probability theory methods. Furthermore, we will introduce an algorithm that speeds up the standard solution for (CNF-SAT)…

Logic in Computer Science · Computer Science 2021-04-26 Hazem J. Alkhatib , Majd N. Bohssas , Rawad H. Hatem , Odey N. Kassam Alhennawi

SARRIGUREN, a new complete algorithm for SAT based on counting clauses (which is valid also for Unique-SAT and #SAT) is described, analyzed and tested. Although existing complete algorithms for SAT perform slower with clauses with many…

Data Structures and Algorithms · Computer Science 2025-04-08 Alfredo Goñi Sarriguren

It is shown that under standard hypotheses, if stochastic approximation iterates remain tight, they converge with probability one to what their o.d.e. limit suggests. A simple test for tightness (and therefore a.s. convergence) is provided.…

Probability · Mathematics 2010-07-28 Sameer Kamal

In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the…

Machine Learning · Computer Science 2026-02-24 Kasper Green Larsen , Markus Engelund Mathiasen , Chirag Pabbaraju , Clement Svendsen

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and…

Statistical Mechanics · Physics 2011-11-09 Jack Raymond , Andrea Sportiello , Lenka Zdeborová

We study the structure of the solution space and behavior of local search methods on random 3-SAT problems close to the SAT/UNSAT transition. Using the overlap measure of similarity between different solutions found on the same problem…

Statistical Mechanics · Physics 2009-11-13 John Ardelius , Erik Aurell , Supriya Krishnamurthy

We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…

Discrete Mathematics · Computer Science 2017-08-04 Jean Cardinal , Jerri Nummenpalo , Emo Welzl