Short proofs for tricky formulas
Acta Informatica
A DNF without regular shortest consensus path
SIAM Journal on Computing
Regular resolution versus unrestricted resolution
SIAM Journal on Computing
Tail bounds for occupancy and the satisfiability threshold conjecture
Random Structures & Algorithms
A machine program for theorem-proving
Communications of the ACM
Size space tradeoffs for resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Optimality of size-width tradeoffs for resolution
Computational Complexity
Regular and general resolution: an improved separation
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
An improved separation of regular resolution from pool resolution and clause learning
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Exponential separations in a hierarchy of clause learning proof systems
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
| Hi-index | 0.00 |
This paper gives a near-optimal separation between regular and unrestricted resolution. The main result is that there is a sequence of sets of clauses $\Pi_1,\Pi_2,\ldots,\Pi_i,\ldots$ for which the minimum regular resolution refutation of $\Pi_i$ has size $2^{\Omega(R_i/(\log R_i)^7\log\log R_i)}$, where $R_i$ is the minimum size of an unrestricted resolution refutation of $\Pi_i$. This improves earlier lower bounds for which the separations proved were of the form $2^{\Omega(\sqrt[3]{R})}$ and $2^{\Omega(\sqrt[4]{R}/(\log R)^3)}$.