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Polynomial Time SAT Decision, Hypergraph Transversals and the Hermitian Rank [chapter]

Nicola Galesi, Oliver Kullmann
2005 Lecture Notes in Computer Science  
We show polynomial time SAT decision of the class of formulas with hermitian rank at most one, applying methods from hypergraph transversal theory.  ...  Combining graph theory and linear algebra, we study SAT problems of low "linear algebra complexity", considering formulas with bounded hermitian rank.  ...  Acknowledgements Part of this work was done while we were visiting the ICTP in Trieste participating in the Thematic Institute of the Complex Systems Network of Excellence (EXYSTENCE): "Algorithms and  ... 
doi:10.1007/11527695_8 fatcat:lbc6dkmybjfhreu3xqbbf3wc7q

Bounds for variables with few occurrences in conjunctive normal forms [article]

Oliver Kullmann, Xishun Zhao
2017 arXiv   pre-print
is open to find the autarky itself in polynomial time.  ...  We try to build a bridge from logic to combinatorics (especially to hypergraph colouring), and we discuss thoroughly the background and open problems, and provide many examples and explanations.  ...  Hypergraph Problem, where every transversal must be "exact", that is, must intersect every hyperedge in exactly one vertex; this problem is decidable in polynomial time by [99] , and thus we get SAT-decision  ... 
arXiv:1408.0629v5 fatcat:tsrsjj7rdvfplnsi7k2vdwex7y

The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

V. Bapst, L. Foini, F. Krzakala, G. Semerjian, F. Zamponi
2013 Physics reports  
This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction.  ...  Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal  ...  Biroli Computations were performed in part at the MesoPSL computing center, with support from Région Ile de France and ANR, in part using HPC resources  ... 
doi:10.1016/j.physrep.2012.10.002 fatcat:s6gnhlt3yzf6xpe3rq6uamqsyy

Constraint satisfaction problems in clausal form: Autarkies, minimal unsatisfiability, and applications to hypergraph inequalities

Oliver Kullmann, Nadia Creignou, Phokion Kolaitis, Heribert Vollmer
2006
First we consider poly-time SAT decision (and fixed-parameter tractability) exploiting matching theory.  ...  Generalised CNFs are considered using such literals, which exclude exactly one possible value from the domain of the variable.  ...  ) decision problem is solvable in polynomial time as shown in [31] ).  ... 
doi:10.4230/dagsemproc.06401.4 fatcat:hheqc43kujavngl2arrdvxouje

Bounds for variables with few occurrences in conjunctive normal forms

Oliver Kullmann, Xishun Zhao
2014 unpublished
We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree of variables in various forms of redundancy-free boolean conjunctive normal  ...  matrix A ′ ". 10) In [54] unfortunately the term "uniform" was (mis)used instead of "regular". polynomial time by [21] , and thus we get SAT-decision for CLS h≤1 in polynomial time.  ...  Question 9.6 Can SAT decision for SED be done in polynomial time? If so, can we also find a satisfying assignment quickly?  ... 
fatcat:njlq5fvevjh7naoabklkpkitnq

Constraint satisfaction problems in clausal form [article]

Oliver Kullmann
2011 pre-print
Main results concern classification of minimally unsatisfiable clause-sets and the relations to the hermitian rank of graphs. Both parts contain also discussions of many open problems.  ...  The first part sets the foundations for the theory of autarkies, with emphasise on matching autarkies. Main results concern various polynomial time results in dependency on the deficiency.  ...  as the hypergraph transversal problem).  ... 
doi:10.3233/fi-2011-428; arXiv:1103.3693v1 fatcat:x6ncma7xo5bhndbmfhmjeyeqty

50 Algebra in Computational Complexity (Dagstuhl Seminar 14391) Manindra Agrawal, Valentine Kabanets, Thomas Thierauf, and Christopher Umans 85 Privacy and Security in an Age of Surveillance (Dagstuhl Perspectives Workshop

Maria-Florina Balcan, Bodo Manthey, Heiko Röglin, Tim Roughgarden, Artur D'avila Garcez, Marco Gori, Pascal Hitzler, Luís Lamb, Bart Preneel, Phillip Rogaway, Mark Ryan, Peter (+5 others)
unpublished
For example, in any 3-SAT formula a fraction of 7/8 of its clauses can always be satisfied by some assignment which can be found in polynomial time.  ...  Michael Forbes considered the question whether the hitting set constructions running in quasi-polynomial time can be improved to polynomial time.  ...  of stochastic Hermitian operators in small space, which is a natural and important problem.  ... 
fatcat:e5wnf6cuhvc3bceegijgut34zm

Dagstuhl Reports, Volume 8, Issue 10, October 2018, Complete Issue [article]

2019
thank all the attendees for their contributions and extend special thanks to the moderators of the breakout sessions and the team of Schloss Dagstuhl for helping to make this seminar a success.  ...  As always, we enjoyed the warm atmosphere, which supports both formal presentations as well as informal exchanges of ideas.  ...  This approach has been studied since a long time and has produced its own important open questions, among them the question whether the minimal transversals of a hypergraph can be enumerated in output-polynomial  ... 
doi:10.4230/dagrep.8.10 fatcat:q5uhtls46rd3zf4cnl4szgxc7y