A simplified way of proving trade-off results for resolution
Information Processing Letters
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
Different approaches to proof systems
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)
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
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Relating proof complexity measures and practical hardness of SAT
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Some trade-off results for polynomial calculus: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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
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A number of works have looked at the relationship between length and space of resolution proofs. A notorious question has been whether the existence of a short proof implies the existence of a proof that can be verified using limited space.In this paper we resolve the question by answering it negatively in the strongest possible way. We show that there are families of 6-CNF formulas of size n, for arbitrarily large n, that have resolution proofs of length O(n) but for which any proof requires space Omega(n / log n). This is the strongest asymptotic separation possible since any proof of length O(n) can always be transformed into a proof in space O(n / log n).Our result follows by reducing the space complexity of so called pebbling formulas over a directed acyclic graph to the black-white pebbling price of the graph.The proof is somewhat simpler than previous results (in particular, those reported in [Nordstrom 2006, Nordstrom and Hastad 2008]) as it uses a slightly different flavor of pebbling formulas which allows for a rather straightforward reduction of proof space to standard black-white pebbling price.