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A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open…

Computational Complexity · Computer Science 2025-12-05 Lijie Chen , Zhenjian Lu , Igor C. Oliveira , Hanlin Ren , Rahul Santhanam

The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…

Computational Complexity · Computer Science 2019-09-12 Libor Barto

We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…

Optimization and Control · Mathematics 2025-10-08 Miroslav Rada , Milan Hladík , Elif Garajová

The (2+p)-Satisfiability (SAT) problem interpolates between different classes of complexity theory and is believed to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a…

Disordered Systems and Neural Networks · Physics 2009-10-31 Remi Monasson , Riccardo Zecchina

We present a deterministic polynomial-time algorithm that solves the 3-satisfiability problem.

Computational Complexity · Computer Science 2012-01-09 Amar Mukherjee

Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…

Computational Complexity · Computer Science 2012-08-03 Maria Ercsey-Ravasz , Zoltan Toroczkai

We show how one can use certain deterministic algorithms for higher-value constraint satisfaction problems (CSPs) to speed up deterministic local search for 3-SAT. This way, we improve the deterministic worst-case running time for 3-SAT to…

Data Structures and Algorithms · Computer Science 2010-07-27 Konstantin Kutzkov , Dominik Scheder

We prove that completing an untimed, unbounded track in TrackMania Nations Forever is NP-complete by using a reduction from 3-SAT and showing that a solution can be checked in polynomial time.

Computational Complexity · Computer Science 2014-11-24 Franck Dernoncourt

It has been hypothesized that $k$-SAT is hard to solve for randomly chosen instances near the "critical threshold", where the clause-to-variable ratio is $2^k \ln 2-\theta(1)$. Feige's hypothesis for $k$-SAT says that for all sufficiently…

Data Structures and Algorithms · Computer Science 2018-10-16 Nikhil Vyas

By the MAXSAT problem, we are given a set $V$ of $m$ variables and a collection $C$ of $n$ clauses over $V$, i.e., a conjunctive normal form ($\textit{CNF}$) formula. We will seek a truth assignment to maximize the number of satisfied…

Computational Complexity · Computer Science 2025-08-05 Yangjun Chen

This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…

Computational Complexity · Computer Science 2019-07-01 Bart M. P. Jansen , Astrid Pieterse

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…

Combinatorics · Mathematics 2017-11-17 Amin Coja-Oghlan , Amir Haqshenas , Samuel Hetterich

Let F be a CNF formula with n variables and m clauses. F is 3-satisfiable if for any 3 clauses in F, there is a truth assignment which satisfies all of them. Lieberherr and Specker (1982) and, later, Yannakakis (1994) proved that in each…

Discrete Mathematics · Computer Science 2012-12-03 Gregory Gutin , Mark Jones , Dominik Scheder , Anders Yeo

Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…

Computational Complexity · Computer Science 2021-05-25 Manoj Kumar

With using of multi-nary logic analytic formulas proposition that "kSAT is in P and could be solved in $O(n^{3.5})$" was proved

Computational Complexity · Computer Science 2012-04-03 Algirdas Antano Maknickas

The field of fine-grained complexity aims at proving conditional lower bounds on the time complexity of computational problems. One of the most popular assumptions, Strong Exponential Time Hypothesis (SETH), implies that SAT cannot be…

Computational Complexity · Computer Science 2023-07-24 Tatiana Belova , Alexander S. Kulikov , Ivan Mihajlin , Olga Ratseeva , Grigory Reznikov , Denil Sharipov

The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula $\varphi$ in CNF such that exactly one literal in each clause is assigned to be "1" and the other literals in the same clause…

Data Structures and Algorithms · Computer Science 2020-12-15 Gordon Hoi

In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…

Computational Complexity · Computer Science 2018-08-20 Chengling Fang , Jiang Liu

We study the computational complexity of fundamental problems over the $p$-adic numbers ${\mathbb Q}_p$ and the $p$-adic integers ${\mathbb Z}_p$. Gu\'epin, Haase, and Worrell proved that checking satisfiability of systems of linear…

Computational Complexity · Computer Science 2025-04-21 Arno Fehm , Manuel Bodirsky

Partially ordered models of time occur naturally in applications where agents or processes cannot perfectly communicate with each other, and can be traced back to the seminal work of Lamport. In this paper we consider the problem of…

Computational Complexity · Computer Science 2023-05-26 Leif Eriksson , Victor Lagerkvist