Filters








12,322 Hits in 6.3 sec

Improved Separations of Regular Resolution from Clause Learning Proof Systems [article]

Maria Luisa Bonet, Sam Buss, Jan Johannsen
2012 arXiv   pre-print
We prove that the graph tautology formulas of Alekhnovich, Johannsen, Pitassi, and Urquhart have polynomial size pool resolution refutations that use only input lemmas as learned clauses and without degenerate  ...  We also prove that these graph tautology formulas can be refuted by polynomial size DPLL proofs with clause learning, even when restricted to greedy, unit-propagating DPLL search.  ...  The class of natural proof systems is known to include common proof systems such as tree-like or regular proofs.  ... 
arXiv:1208.2469v1 fatcat:m5zmky2n75dvvfv54jdd2ba3xu

Improved Separations of Regular Resolution from Clause Learning Proof Systems

M. L. Bonet, S. Buss, J. Johannsen
2014 The Journal of Artificial Intelligence Research  
We prove that the guarded, xor-ified pebbling tautology clauses, which Urquhart proved are hard for regular resolution, as well as the guarded graph tautology clauses of Alekhnovich, Johannsen, Pitassi  ...  This refutes the conjecture that the guarded graph tautology clauses or the guarded xor-ified pebbling tautology clauses can be used to separate CDCL without restarts from general resolution.  ...  The class of natural proof systems is known to include common proof systems such as tree-like or regular proofs.  ... 
doi:10.1613/jair.4260 fatcat:ntgw44t45nacxahqutvpegzs2u

Understanding the Power of Clause Learning

Paul Beame, Henry A. Kautz, Ashish Sabharwal
2003 International Joint Conference on Artificial Intelligence  
This paper presents the first precise characterization of clause learning as a proof system, and begins the task of understanding its power.  ...  We also show that without restarts but with a new learning scheme, clause learning can provide exponentially smaller proofs than regular resolution, which itself is known to be much stronger than ordinary  ...  We then show that if a formula exponentially separates general resolution from regular resolution, its extension exponentially separates clause learning from regular resolution.  ... 
dblp:conf/ijcai/BeameKS03 fatcat:uhaiyq3wffbpvahd3o6uh3rbnu

An Improved Separation of Regular Resolution from Pool Resolution and Clause Learning [article]

Maria Luisa Bonet, Sam Buss
2012 arXiv   pre-print
We prove that the graph tautology principles of Alekhnovich, Johannsen, Pitassi and Urquhart have polynomial size pool resolution refutations that use only input lemmas as learned clauses and without degenerate  ...  We also prove that these graph tautology principles can be refuted by polynomial size DPLL proofs with clause learning, even when restricted to greedy, unit-propagating DPLL search.  ...  The class of natural proof systems is known to include common proof systems such as tree-like or regular proofs.  ... 
arXiv:1202.2296v2 fatcat:g4pbue3gzjcn5p2d3xfz4gpsoa

Towards NP–P via proof complexity and search

Samuel R. Buss
2012 Annals of Pure and Applied Logic  
This is a survey of work on proof complexity and proof search from a logicoalgorithmic viewpoint, as motivated by the P versus NP problem.  ...  We discuss propositional proof complexity, Cook's program, proof automatizability, proof search, algorithms for satisfiability, and the state of the art of our (in)ability to separate P and NP.  ...  Razborov for comments on an earlier draft of this paper. We also thank two anonymous referees for their careful reading and useful comments.  ... 
doi:10.1016/j.apal.2011.09.009 fatcat:oud37acsqfgrdio62ir6ci24xi

Resolution Trees with Lemmas: Resolution Refinements that Characterize DLL Algorithms with Clause Learning

Samuel Buss, Jan Hoffmann, Jan Johannsen, Jan Krajícek
2008 Logical Methods in Computer Science  
For regular proofs, an exponential separation between regular dag-like resolution and both regular WRTL and regular WRTI is given.  ...  A general form of clause learning, called DLL-Learn, is defined that is equivalent to regular WRTL.  ...  Our definition of variable extensions is inspired by the proof trace extensions of Beame et al. [2] that were used to separate DLL with clause learning from regular resolution dags.  ... 
doi:10.2168/lmcs-4(4:13)2008 fatcat:6c5bs7t2brearnfcaskwrj7f24

An Improved Separation of Regular Resolution from Pool Resolution and Clause Learning [chapter]

Maria Luisa Bonet, Sam Buss
2012 Lecture Notes in Computer Science  
We prove that the graph tautology principles of Alekhnovich, Johannsen, Pitassi and Urquhart have polynomial size pool resolution refutations that use only input lemmas as learned clauses and without degenerate  ...  We also prove that these graph tautology principles can be refuted by polynomial size DPLL proofs with clause learning, even when restricted to greedy, unit-propagating DPLL search. during which these  ...  The class of natural proof systems is known to include common proof systems such as tree-like or regular proofs.  ... 
doi:10.1007/978-3-642-31612-8_5 fatcat:coiw5b3u55hqfpk6k46r4jlax4

The state of SAT

Henry Kautz, Bart Selman
2007 Discrete Applied Mathematics  
This foreword reviews the current state of satisfiability testing and places the papers in this issue in context.  ...  The papers in this special issue originated at SAT 2001, the Fourth International Symposium on the Theory and Applications of Satisfiability Testing.  ...  However, the questions of whether clause learning is strictly stronger than regular resolution-that is, whether or not there are also formulas with short regular proofs but long clause proofs-and whether  ... 
doi:10.1016/j.dam.2006.10.004 fatcat:uouc5yqwlbhpbpd5g25ka3mdia

Ten Challenges Redux: Recent Progress in Propositional Reasoning and Search [chapter]

Henry Kautz, Bart Selman
2003 Lecture Notes in Computer Science  
In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies.  ...  However, the questions of whether clause learning is strictly stronger than regular resolution -that is, whether or not there are also formulas with short regular proofs but long clause proofs -and whether  ...  The result was, in fact, even stronger: they showed that there are formulas with short clause learning proofs that require exponentially large regular resolution proofs.  ... 
doi:10.1007/978-3-540-45193-8_1 fatcat:a6eqq3kh6nalpfowg4pfc3xkhu

Exponential Separations in a Hierarchy of Clause Learning Proof Systems [chapter]

Jan Johannsen
2013 Lecture Notes in Computer Science  
Resolution trees with lemmas (RTL) are a resolution-based propositional proof system that is related to the DPLL algorithm with clause learning.  ...  For every k up to O(log n), an exponential separation between the proof systems RTL(k) and RTL(k + 1) is shown.  ...  Conclusion We have shown that for resolution trees with lemmas { a resolution-based propositional proof system that forms the basis of a family of proof systems capturing the complexity of clause-learning  ... 
doi:10.1007/978-3-642-39071-5_5 fatcat:kr5chw2kzfhr3fbvitadihw3xy

Trade-offs Between Time and Memory in a Tighter Model of CDCL SAT Solvers [chapter]

Jan Elffers, Jan Johannsen, Massimo Lauria, Thomas Magnard, Jakob Nordström, Marc Vinyals
2016 Lecture Notes in Computer Science  
A long line of research has studied the power of conflictdriven clause learning (CDCL) and how it compares to the resolution proof system in which it searches for proofs.  ...  CDCL without any restarts using the standard 1UIP clause learning scheme, and the (in some cases tightly matching) lower bounds hold for arbitrarily frequent restarts and arbitrary clause learning schemes  ...  Acknowledgements We are grateful to the anonymous SAT conference reviewers for detailed comments that helped improve the exposition in this paper.  ... 
doi:10.1007/978-3-319-40970-2_11 fatcat:4jiqks3o7rgsrim2njfx36rt54

On Linear Resolution

Sam Buss, Jan Johannsen
2017 Journal on Satisfiability, Boolean Modeling and Computation  
We discuss the relationship between linear resolution, s-linear resolution and other fragments of resolution, including tree-like resolution, regular resolution and general resolution.  ...  We present polynomial-size linear resolution proofs of the ordering tautologies (also known as "graph tautologies"), and the guarded ordering tautologies.  ...  We thank Alasdair Urquhart for suggesting the problem of linear resolution to us. We also thank the referees for useful comments and suggestions.  ... 
doi:10.3233/sat190112 fatcat:x4a4auiayjed5kewlv74npix4q

Towards Understanding and Harnessing the Potential of Clause Learning

P. Beame, H. Kautz, A. Sabharwal
2004 The Journal of Artificial Intelligence Research  
This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the well-studied resolution proof system  ...  In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property.  ...  Acknowledgments The authors wish to thank the anonymous referees for providing useful comments and for pointing out the existence of short tree-like RES(k) proofs of pebbling formulas.  ... 
doi:10.1613/jair.1410 fatcat:q4ub33w2ezfwlcacmymanlqmlm

Simplified and Improved Separations Between Regular and General Resolution by Lifting [chapter]

Marc Vinyals, Jan Elffers, Jan Johannsen, Jakob Nordström
2020 Lecture Notes in Computer Science  
We give a significantly simplified proof of the exponential separation between regular and general resolution of Alekhnovich et al. (2007) as a consequence of a general theorem lifting proof depth to regular  ...  proof length in resolution.  ...  We also acknowledge the important role played by the Dagstuhl seminar 18051 "Proof Complexity," where some of this work was performed.  ... 
doi:10.1007/978-3-030-51825-7_14 fatcat:zyk7tftjajbijm5tins3wwo2iq

Space in weak propositional proof systems

Ilario Bonacina
2016 Bulletin of the European Association for Theoretical Computer Science  
This year's award went to Ilario Bonacina for his thesis Space in weak propositional proof systems, which was supervised by Nicola Galesi at the University of Rome "La Sapienza".  ...  Ilario's thesis contributes to a classic and deep topic in theoretical computer science, and settles natural questions on the space complexity of proofs using Resolution and the Polynomial Calculus that  ...  Our results both improve and simplify the strong size lower bound from Beck and Impagliazzo [5] and improve the asymptotic of the k for tree-like and regular Resolution.  ... 
dblp:journals/eatcs/Bonacina16 fatcat:7oxgzcxtdnf4bfpncyd27bhshe
« Previous Showing results 1 — 15 out of 12,322 results