Generalising and Unifying SLUR and Unit-Refutation Completeness

The class \(\mathcal{SLUR}\) (Single Lookahead Unit Resolution) was introduced in [22] as an umbrella class for efficient SAT solving.[7,2] extended this class in various ways to hierarchies covering all of CNF (all clause-sets). We introduce a hierarchy \(\mathcal{SLUR}_k\) which we argue is the natural “limit” of such approaches.

[1]  Hans van Maaren,et al.  A Short Note on Some Tractable Cases of the Satisfiability Problem , 2000, Inf. Comput..

[2]  Joao Marques-Silva,et al.  Knowledge Compilation with Empowerment , 2012, SOFSEM.

[3]  Heribert Vollmer,et al.  Complexity of Constraints - An Overview of Current Research Themes [Result of a Dagstuhl Seminar] , 2008, Complexity of Constraints.

[4]  Toby Walsh,et al.  Handbook of satisfiability , 2009 .

[5]  Hans Kleine Büning.  On generalized Horn formulas and k-resolution , 1993, Theor. Comput. Sci..

[6]  Adnan Darwiche,et al.  On the power of clause-learning SAT solvers as resolution engines , 2011, Artif. Intell..

[7]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[8]  Václav Vlcek,et al.  On hierarchies over the SLUR class , 2012, ISAIM.

[9]  Peter L. Hammer,et al.  Boolean Functions - Theory, Algorithms, and Applications , 2011, Encyclopedia of mathematics and its applications.

[10]  Piotr Lipinski,et al.  Improving Watermark Resistance against Removal Attacks Using Orthogonal Wavelet Adaptation , 2012, SOFSEM.

[11]  Allen Van Gelder,et al.  A perspective on certain polynomial-time solvable classes of satisfiability , 2003, Discret. Appl. Math..

[12]  Maria Luisa Bonet,et al.  Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence (2008) , 2022 .

[13]  Lawrence J. Henschen,et al.  Unit Refutations and Horn Sets , 1974, JACM.

[14]  Toby Walsh,et al.  Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications , 2009 .

[15]  John Franco.  Relative size of certain polynomial time solvable subclasses of satisfiability , 1996, Satisfiability Problem: Theory and Applications.

[16]  Oliver Kullmann,et al.  Towards a better understanding of hardness , 2011 .

[17]  Oliver Kullmann,et al.  Upper and Lower Bounds on the Complexity of Generalised Resolution and Generalised Constraint Satisfaction Problems , 2004, Annals of Mathematics and Artificial Intelligence.

[18]  Oliver Kullmann,et al.  Generalising Unit-Refutation Completeness and SLUR via Nested Input Resolution , 2013, Journal of Automated Reasoning.

[19]  Alvaro del Val.  Tractable Databases: How to Make Propositional Unit Resolution Complete Through Compilation , 1994, KR.

[20]  Oliver Kullmann.  Present and Future of Practical SAT Solving , 2008, Complexity of Constraints.

[21]  Oliver Kullmann,et al.  Investigating a general hierarchy of polynomially decidable classes of CNF's based on short tree-like resolution proofs , 1999, Electron. Colloquium Comput. Complex..

[22]  Toby Walsh,et al.  Circuit Complexity and Decompositions of Global Constraints , 2009, IJCAI.

[23]  Hans Kleine Büning,et al.  Minimal Unsatisfiability and Autarkies , 2009, Handbook of Satisfiability.

[24]  Panos M. Pardalos,et al.  Satisfiability problem : theory and applications : DIMACS workshop, March 11-13, 1996 , 1997 .

[25]  Ondrej Cepek,et al.  Properties of SLUR Formulae , 2012, SOFSEM.

[26]  Ondrej Cepek,et al.  Known and new classes of generalized Horn formulae with polynomial recognition and SAT testing , 2005, Discret. Appl. Math..

[27]  Oliver Kullmann,et al.  Towards a better understanding of SAT translations , 2011 .

[28]  Fred S. Annexstein,et al.  On Finding Solutions for Extended Horn Formulas , 1995, Inf. Process. Lett..