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Satisfiability Testing (SAT) techniques are well-established in classical computing where they are used to solve a broad variety of problems, e.g., in the design of classical circuits and systems. Analogous to the classical realm, quantum…

Quantum Physics · Physics 2023-01-11 Lucas Berent , Lukas Burgholzer , Robert Wille

A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in…

Computational Complexity · Computer Science 2017-07-04 Bernd R. Schuh

In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether…

Data Analysis, Statistics and Probability · Physics 2010-02-02 K. A. Zweig , G. Palla , T. Vicsek

We explore the possibility of accelerating the formal verification of classical programs with a quantum computer. A common source of security flaws stems from the existence of common programming errors like use after free, null-pointer…

Quantum Physics · Physics 2026-05-06 Sebastian Issel , Kilian Tscharke , Pascal Debus

The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known…

Quantum Physics · Physics 2007-12-17 Yi-Kai Liu

NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary…

Data Structures and Algorithms · Computer Science 2017-04-07 Belal Qasemi

This report presents VLSAT-3 (an acronym for "Very Large Boolean SATisfiability problems"),the third part of a benchmark suite to be used in scientific experimentsand software competitions addressing SAT and SMT (Satisfiability Modulo…

Data Structures and Algorithms · Computer Science 2021-12-10 Pierre Bouvier

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…

Computational Complexity · Computer Science 2013-07-29 Lu-Lu Wu , Hai-Jun Zhou , Mikko Alava , Erik Aurell , Pekka Orponen

The use of Boolean Satisfiability (SAT) solver for hardware verification incurs exponential run-time in several instances. In this work we have proposed an efficient quantum SAT (qSAT) solver for equivalence checking of Boolean circuits…

Quantum Physics · Physics 2026-05-19 Abhoy Kole , Mohammed E. Djeridane , Lennart Weingarten , Kamalika Datta , Rolf Drechsler

As contemporary quantum computers do not possess error correction, any calculation performed by these devices can be considered an involuntary approximation. To solve a problem on a quantum annealer, it has to be expressed as an instance of…

Recently, Dunjko et al.(PRL, 2018) proposed an algorithm for accelerating the solution of 3-satisfiability problems using a small-scale quantum computer. In this paper, we design a distributed quantum-classical hybrid algorithm for solving…

Quantum Physics · Physics 2026-04-16 Huaijing Huang , Daowen Qiu , Le Luo , Paulo Mateus

We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with…

Quantum Physics · Physics 2009-02-20 Dorit Aharonov , Daniel Gottesman , Sandy Irani , Julia Kempe

This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements,…

Computational Complexity · Computer Science 2018-01-25 Keum-Bae Cho

In this paper we define a restricted version of Monotone NAE-3SAT and show that it remains NP-Complete even under that restriction. We expect this result would be useful in proving NP-Completeness results for problems on $k$-colourable…

Computational Complexity · Computer Science 2010-03-30 Peiyush Jain

We show enough evidence that a structured version of Adiabatic Quantum Computation (AQC) is efficient for most satisfiability problems. More precisely, when the success probability is fixed beforehand, the computational resources grow…

Quantum Physics · Physics 2008-12-10 Juan Jose Garcia-Ripoll , Mari Carmen Bañuls

The satisfaction probability Pr[$\phi$] := Pr$_{\beta:vars(\phi) \to \{0,1\}}[\beta\models \phi]$ of a propositional formula $\phi$ is the likelihood that a random assignment $\beta$ makes the formula true. We study the complexity of the…

Computational Complexity · Computer Science 2024-08-12 Till Tantau

We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…

Computational Complexity · Computer Science 2011-12-14 Florent Madelaine , Barnaby Martin , Juraj Stacho

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…

Computational Complexity · Computer Science 2021-11-16 Shyan Akmal , Ryan Williams

The problem of identifying the satisfiability threshold of random $3$-SAT formulas has received a lot of attention during the last decades and has inspired the study of other threshold phenomena in random combinatorial structures. The…

Combinatorics · Mathematics 2024-11-07 Ioannis Caragiannis , Nick Gravin , Zhile Jiang

We determine the classical and quantum complexities of a specific ensemble of three-satisfiability problems with a unique satisfying assignment for up to N=100 and N=80 variables, respectively. In the classical limit we employ generalized…

Statistical Mechanics · Physics 2015-05-27 T. Neuhaus , M. Peschina , K. Michielsen , H. De Raedt