Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
Many hard examples for resolution
Journal of the ACM (JACM)
A guided tour of Chernoff bounds
Information Processing Letters
0-1 laws and decision problems for fragments of second-order logic
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
On the expressive power of Datalog: tools and a case study
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A restricted second order logic for finite structures
Information and Computation
A sharp threshold for k-colorability
Random Structures & Algorithms
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Information and Computation
Space Complexity in Propositional Calculus
SIAM Journal on Computing
A Game-Theoretic Approach to Constraint Satisfaction
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Lower bounds for the weak Pigeonhole principle and random formulas beyond resolution
Information and Computation
Random CNF's are Hard for the Polynomial Calculus
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Examples of hard tautologies in the propositional calculus
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Space Complexity of Random Formulae in Resolution
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
On digraph coloring problems and treewidth duality
European Journal of Combinatorics
From High Girth Graphs to Hard Instances
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Generating hard SAT/CSP instances using expander graphs
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
On the Relative Strength of Pebbling and Resolution
ACM Transactions on Computational Logic (TOCL)
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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A descriptive complexity approach to random 3-SAT is initiated. We show that unsatisfiability of any significant fraction of random 3-CNF formulas cannot be certified by any property that is expressible in Datalog. Combined with the known relationship between the complexity of constraint satisfaction problems and expressibility in Datalog, our result implies that any constraint propagation algorithm working with small constraints will fail to certify unsatisfiability almost always. Our result is a consequence of designing a winning strategy for one of the players in the existential pebble game. The winning strategy makes use of certain extension axioms that we introduce and hold almost surely on a random 3-CNF formula. The second contribution of our work is the connection between finite model theory and propositional proof complexity. To make this connection explicit, we establish a tight relationship between the number of pebbles needed to win the game and the width of the Resolution refutations. As a consequence to our result and the known size--width relationship in Resolution, we obtain new proofs of the exponential lower bounds for Resolution refutations of random 3-CNF formulas and the Pigeonhole Principle.