Journal of the ACM (JACM)
Many hard examples for resolution
Journal of the ACM (JACM)
Resolution proofs of generalized pigeonhole principles. (Note)
Theoretical Computer Science
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A machine program for theorem-proving
Communications of the ACM
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems
SIAM Journal on Computing
Resolution and the Weak Pigeonhole Principle
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
A Study of Proof Search Algorithms for Resolution and Polynomial Calculus
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An Optimal Lower Bound for Resolution with 2-Conjunctions
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
On the Complexity of Resolution with Bounded Conjunctions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The Complexity of Resolution with Generalized Symmetry Rules
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On the Automatizability of Resolution and Related Propositional Proof Systems
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Lower bounds for the weak Pigeonhole principle and random formulas beyond resolution
Information and Computation
Optimality of size-width tradeoffs for resolution
Computational Complexity
Resolution lower bounds for the weak functional pigeonhole principle
Theoretical Computer Science - Logic and complexity in computer science
A combinatorial characterization of treelike resolution space
Information Processing Letters
Resolution lower bounds for the weak pigeonhole principle
Journal of the ACM (JACM)
On sufficient conditions for unsatisfiability of random formulas
Journal of the ACM (JACM)
Optimal length tree-like resolution refutations for 2SAT formulas
ACM Transactions on Computational Logic (TOCL)
On the automatizability of resolution and related propositional proof systems
Information and Computation
A sharp threshold in proof complexity yields lower bounds for satisfiability search
Journal of Computer and System Sciences - STOC 2001
Resolution lower bounds for perfect matching principles
Journal of Computer and System Sciences - Special issue on computational complexity 2002
On the complexity of resolution with bounded conjunctions
Theoretical Computer Science
Lower bounds for k-DNF resolution on random 3-CNFs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Annals of Mathematics and Artificial Intelligence
The resolution complexity of random graphk-colorability
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Typical case complexity of satisfiability algorithms and the threshold phenomenon
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Narrow proofs may be spacious: separating space and width in resolution
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Many hard examples in exact phase transitions
Theoretical Computer Science
Exponential Lower Bounds for the Running Time of DPLL Algorithms on Satisfiable Formulas
Journal of Automated Reasoning
Random constraint satisfaction: Easy generation of hard (satisfiable) instances
Artificial Intelligence
Artificial Intelligence
Foundations and Trends® in Theoretical Computer Science
A combinatorial characterization of resolution width
Journal of Computer and System Sciences
Towards an optimal separation of space and length in resolution
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Resolution Width and Cutting Plane Rank Are Incomparable
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
From High Girth Graphs to Hard Instances
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Note: Finding a tree structure in a resolution proof is NP-complete
Theoretical Computer Science
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Random SAT Instances à la Carte
Proceedings of the 2008 conference on Artificial Intelligence Research and Development: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence
Width-Based Restart Policies for Clause-Learning Satisfiability Solvers
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
A simplified way of proving trade-off results for resolution
Information Processing Letters
Cutting Planes and the Parameter Cutwidth
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Combinatorial Problems for Horn Clauses
Graph Theory, Computational Intelligence and Thought
Consistency and random constraint satisfaction models
Journal of Artificial Intelligence Research
A simple model to generate hard satisfiable instances
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
The resolution complexity of random graph k-colorability
Discrete Applied Mathematics
Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
Discrete Applied Mathematics
ACM Transactions on Computation Theory (TOCT)
Complexity of propositional proofs under a promise
ACM Transactions on Computational Logic (TOCL)
Hardness amplification in proof complexity
Proceedings of the forty-second ACM symposium on Theory of computing
Heuristics for resolution in propositional logic
KI'09 Proceedings of the 32nd annual German conference on Advances in artificial intelligence
Mean-payoff games and propositional proofs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the power of clause-learning SAT solvers as resolution engines
Artificial Intelligence
Mean-payoff games and propositional proofs
Information and Computation
The complexity of inversion of explicit goldreich's function by DPLL algorithms
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Parameterized complexity of DPLL search procedures
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
On minimal unsatisfiability and time-space trade-offs for k-DNF resolution
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On the relative efficiency of DPLL and OBDDs with axiom and join
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Boolean rings for intersection-based satisfiability
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Pool resolution and its relation to regular resolution and DPLL with clause learning
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Simulating cutting plane proofs with restricted degree of falsity by resolution
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Resolution tunnels for improved SAT solver performance
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Input distance and lower bounds for propositional resolution proof length
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Exact thresholds for DPLL on random XOR-SAT and NP-complete extensions of XOR-SAT
Theoretical Computer Science
Proof complexity of non-classical logics
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
On the Relative Strength of Pebbling and Resolution
ACM Transactions on Computational Logic (TOCL)
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Two techniques for minimizing resolution proofs
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Preliminary report on input cover number as a metric for propositional resolution proofs
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Local search for unsatisfiability
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Knowledge compilation with empowerment
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Lower bounds for width-restricted clause learning on formulas of small width
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
Proof complexity of non-classical logics
ESSLLI'10 Proceedings of the 2010 conference on ESSLLI 2010, and ESSLLI 2011 conference on Lectures on Logic and Computation
Short Propositional Refutations for Dense Random 3CNF Formulas
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Complexity of propositional proofs under a promise
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
A general model and thresholds for random constraint satisfaction problems
Artificial Intelligence
Relating proof complexity measures and practical hardness of SAT
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Some trade-off results for polynomial calculus: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Parameterized Complexity of DPLL Search Procedures
ACM Transactions on Computational Logic (TOCL)
The proof-search problem between bounded-width resolution and bounded-degree semi-algebraic proofs
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
On the resolution complexity of graph non-isomorphism
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
A rank lower bound for cutting planes proofs of ramsey's theorem
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Towards an understanding of polynomial calculus: new separations and lower bounds
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Theory of Computing Systems
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The widthof a Resolution proof is defined to be the maximal number of literals in any clause of the proof. In this paper, we relate proof width to proof length (=size), in both general Resolution, and its tree-like variant. The following consequences of these relations reveal width as a crucial “resource” of Resolution proofs.In one direction, the relations allow us to give simple, unified proofs for almost all known exponential lower bounds on size of resolution proofs, as well as several interesting new ones. They all follow from width lower bounds, and we show how these follow from natural expansion property of clauses of the input tautology.In the other direction, the width-size relations naturally suggest a simple dynamic programming procedure for automated theorem proving—one which simply searches for small width proofs. This relation guarantees that the runnuing time (and thus the size of the produced proof) is at most quasi-polynomial in the smallest tree-like proof. This algorithm is never much worse than any of the recursive automated provers (such as DLL) used in practice. In contrast, we present a family of tautologies on which it is exponentially faster.