STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Hard problems for CSP Algorithms
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Short proofs are narrow—resolution made simple
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Initial experiments in stochastic satisfiability
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
A lower bound for DLL algorithms for k-SAT (preliminary version)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Regular resolution lower bounds for the weak pigeonhole principle
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Information and Computation
Size space tradeoffs for resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Resolution lower bounds for the weak pigeonhole principle
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Resolution Proofs of Matching Principles
Annals of Mathematics and Artificial Intelligence
Some interesting research directions in satisfiability
Annals of Mathematics and Artificial Intelligence
Stochastic Boolean Satisfiability
Journal of Automated Reasoning
A syntactical proof of the marriage lemma
Theoretical Computer Science
ASIAN '02 Proceedings of the7th Asian Computing Science Conference on Advances in Computing Science: Internet Computing and Modeling, Grid Computing, Peer-to-Peer Computing, and Cluster
Recognizing More Unsatisfiable Random 3-SAT Instances Efficiently
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Lower Bounds for the Weak Pigeonhole Principle Beyond Resolution
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
On the Complexity of Resolution with Bounded Conjunctions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Efficient Recognition of Random Unsatisfiable k-SAT Instances by Spectral Methods
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Lower Bounds for Space in Resolution
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
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
Monotone Proofs of the Pigeon Hole Principle
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Lower bounds for the weak Pigeonhole principle and random formulas beyond resolution
Information and Computation
A Study of Proof Search Algorithms for Resolution and Polynomial Calculus
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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
Space complexity of random formulae in resolution
Random Structures & Algorithms
A combinatorial characterization of treelike resolution space
Information Processing Letters
Annals of Mathematics and Artificial Intelligence
Mutilated chessboard problem is exponentially hard for resolution
Theoretical Computer Science
Resolution lower bounds for the weak pigeonhole principle
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
On the complexity of resolution with bounded conjunctions
Theoretical Computer Science
The satisfiability threshold for randomly generated binary constraint satisfaction problems
Random Structures & Algorithms
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
Conjunctive query evaluation by search-tree revisited
Theoretical Computer Science
Artificial Intelligence
A combinatorial characterization of resolution width
Journal of Computer and System Sciences
What Is a Real-World SAT Instance?
Proceedings of the 2007 conference on Artificial Intelligence Research and Development
Optimal Length Resolution Refutations of Difference Constraint Systems
Journal of Automated Reasoning
Width-Based Restart Policies for Clause-Learning Satisfiability Solvers
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Measuring the hardness of SAT instances
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
The resolution complexity of random graph k-colorability
Discrete Applied Mathematics
Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
Discrete Applied Mathematics
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Mean-payoff games and propositional proofs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Mean-payoff games and propositional proofs
Information and Computation
Parameterized complexity of DPLL search procedures
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Relativisation provides natural separations for resolution-based proof systems
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Width versus size in resolution proofs
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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
Conjunctive query evaluation by search tree revisited
ICDT'05 Proceedings of the 10th international conference on Database Theory
Time-space tradeoffs in resolution: superpolynomial lower bounds for superlinear space
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Strong ETH holds for regular resolution
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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
Implicit learning of common sense for reasoning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
| Hi-index | 0.00 |
We give simple new lower bounds on the lengths of resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds significantly extend the range of formula sizes for which non-trivial lower bounds are known. For example, we show that with probability approaching 1, any resolution refutation of a randomly chosen 3-CNF formula with at most n/sup 6/5-/spl epsiv// clauses requires exponential size. Previous bounds applied only when the number of clauses was at most linear in the number of variables. For the pigeonhole principle our bound is a small improvement over previous bounds. Our proofs are more elementary than previous arguments, and establish a connection between resolution proof size and maximum clause size.