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The quantified constraint satisfaction problem $\mathrm{QCSP}(\mathcal{A})$ is the problem to decide whether a positive Horn sentence, involving nothing more than the two quantifiers and conjunction, is true on some fixed structure…

Logic in Computer Science · Computer Science 2017-01-11 Barnaby D. Martin , Hubie Chen , Florent R. Madelaine

The constraint satisfaction problem, parameterized by a relational structure, provides a general framework for expressing computational decision problems. Already the restriction to the class of all finite structures forms an interesting…

Logic in Computer Science · Computer Science 2024-02-15 Jakub Rydval , Žaneta Semanišinová , Michał Wrona

The Boolean Satisfiability (SAT) problem is the canonical NP-complete problem and is fundamental to computer science, with a wide array of applications in planning, verification, and theorem proving. Developing and evaluating practical SAT…

Machine Learning · Computer Science 2019-10-31 Jiaxuan You , Haoze Wu , Clark Barrett , Raghuram Ramanujan , Jure Leskovec

The CNF formula satisfiability problem (CNF-SAT) has been reduced to many fundamental problems in P to prove tight lower bounds under the Strong Exponential Time Hypothesis (SETH). Recently, the works of Abboud, Hansen, Vassilevska W. and…

Computational Complexity · Computer Science 2020-08-31 Daniel Gibney , Gary Hoppenworth , Sharma V. Thankachan

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

We determine the asymptotical satisfiability probability of a random at-most-k-Horn formula, via a probabilistic analysis of a simple version, called PUR, of positive unit resolution. We show that for $k=k(n)\rightarrow \infty$ the problem…

Data Structures and Algorithms · Computer Science 2025-09-16 Gabriel Istrate

Posibilistic logic is the most extended approach to handle uncertain and partially inconsistent information. Regarding normal forms, advances in possibilistic reasoning are mostly focused on clausal form. Yet, the encoding of real-world…

Artificial Intelligence · Computer Science 2021-11-16 Gonzalo E. Imaz

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and H\r{a}stad roved a result known as "$(2+\varepsilon)$-SAT is NP-hard" [FOCS'14/SICOMP'17]. They showed that the problem of distinguishing k-CNF formulas…

Discrete Mathematics · Computer Science 2021-09-10 Alex Brandts , Marcin Wrochna , Stanislav Živný

The proof of a program property can be reduced to the proof of satisfiability of a set of constrained Horn clauses (CHCs) which can be automatically generated from the program and the property. In this paper we have conducted a case study…

Logic in Computer Science · Computer Science 2019-07-10 Emanuele De Angelis , Fabio Fioravanti , Alberto Pettorossi , Maurizio Proietti

A variant of the well-known Assignment Problem is studied in this paper, where pairs of assignments are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which models real…

Optimization and Control · Mathematics 2025-06-06 Roberto Montemanni , Derek H. Smith

In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program…

Programming Languages · Computer Science 2016-07-18 Bishoksan Kafle , John P. Gallagher , Pierre Ganty

A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…

Disordered Systems and Neural Networks · Physics 2009-11-07 W. Barthel , A. K. Hartmann , M. Leone , F. Ricci-Tersenghi , M. Weigt , R. Zecchina

Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is…

Optimization and Control · Mathematics 2016-11-17 Benjamin Recht , Weiyu Xu , Babak Hassibi

Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art…

Programming Languages · Computer Science 2017-08-08 Alexey Bakhirkin , David Monniaux

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side, especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT…

Logic in Computer Science · Computer Science 2020-02-25 Anastasios Kyrillidis , Anshumali Shrivastava , Moshe Y. Vardi , Zhiwei Zhang

The question of whether the complexity class P is equal to the complexity class NP has been a seemingly intractable problem for over 4 decades. It has been clear that if an algorithm existed that would solve the problems in the NP class in…

Computational Complexity · Computer Science 2015-06-04 Jason W. Steinmetz

Catamorphisms are functions that are recursively defined on list and trees and, in general, on Algebraic Data Types (ADTs), and are often used to compute suitable abstractions of programs that manipulate ADTs. Examples of catamorphisms…

Logic in Computer Science · Computer Science 2025-02-19 Emanuele De Angelis , Fabio Fioravanti , Alberto Pettorossi , Maurizio Proietti

We report on work in progress on automatic procedures for proving properties of programs written in higher-order functional languages. Our approach encodes higher-order programs directly as first-order SMT problems over Horn clauses. It is…

Logic in Computer Science · Computer Science 2013-06-25 Nikolaj Bjorner , Ken McMillan , Andrey Rybalchenko

A multiset of literals, called a clause, is \emph{strongly satisfied} by an assignment if \emph{no} literal evaluates to false. Finding an assignment that maximises the number of strongly satisfied clauses is NP-hard. We present a simple…

Data Structures and Algorithms · Computer Science 2026-03-02 Tamio-Vesa Nakajima , Stanislav Živný

Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…

Computational Complexity · Computer Science 2020-10-05 Dmitriy Zhuk