Journal of the ACM (JACM)
On the complexity of cutting-plane proofs
Discrete Applied Mathematics
Many hard examples for resolution
Journal of the ACM (JACM)
SIAM Journal on Computing
Search Problems in the Decision Tree Model
SIAM Journal on Discrete Mathematics
Lower bounds for cutting planes proofs with small coefficients
STOC '95 Proceedings of the twenty-seventh 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
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Communication complexity
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)
Lower bounds for the polynomial calculus and the Gröbner basis algorithm
Computational Complexity
Lower bounds for the polynomial calculus
Computational Complexity
A machine program for theorem-proving
Communications of the ACM
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Information and Computation
Space Complexity in Propositional Calculus
SIAM Journal on Computing
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems
SIAM Journal on Computing
Separation of the monotone NC hierarchy
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Optimality of size-width tradeoffs for resolution
Computational Complexity
Informational Complexity and the Direct Sum Problem for Simultaneous Message Complexity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Lower Bounds for Polynomial Calculus: Non-Binomial Case
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Space complexity of random formulae in resolution
Random Structures & Algorithms
A Switching Lemma for Small Restrictions and Lower Bounds for k-DNF Resolution
SIAM Journal on Computing
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
On the complexity of resolution with bounded conjunctions
Theoretical Computer Science
Lower Bounds for Lovász-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity
SIAM Journal on Computing
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
Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications
PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials
Journal of Symbolic Computation
Improved Separations between Nondeterministic and Randomized Multiparty Communication
ACM Transactions on Computation Theory (TOCT)
A simplified way of proving trade-off results for resolution
Information Processing Letters
Size-Space Tradeoffs for Resolution
SIAM Journal on Computing
Narrow Proofs May Be Spacious:Separating Space and Width in Resolution
SIAM Journal on Computing
Storage requirements for deterministic polynomialtime recognizable languages
Journal of Computer and System Sciences
Hardness amplification in proof complexity
Proceedings of the forty-second ACM symposium on Theory of computing
Using CSP look-back techniques to solve real-world SAT instances
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
On the power of clause-learning SAT solvers as resolution engines
Artificial Intelligence
Clause-learning algorithms with many restarts and bounded-width resolution
Journal of Artificial Intelligence Research
Lower bounds for width-restricted clause learning on small width formulas
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
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
Space Complexity in Polynomial Calculus
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
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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An active line of research in proof complexity over the last decade has been the study of proof space and trade-offs between size and space. Such questions were originally motivated by practical SAT solving, but have also led to the development of new theoretical concepts in proof complexity of intrinsic interest and to results establishing nontrivial relations between space and other proof complexity measures. By now, the resolution proof system is fairly well understood in this regard, as witnessed by a sequence of papers leading up to [Ben-Sasson and Nordstrom 2008, 2011] and [Beame, Beck, and Impagliazzo 2012]. However, for other relevant proof systems in the context of SAT solving, such as polynomial calculus (PC) and cutting planes (CP), very little has been known. Inspired by [BN08, BN11], we consider CNF encodings of so-called pebble games played on graphs and the approach of making such pebbling formulas harder by simple syntactic modifications. We use this paradigm of hardness amplification to make progress on the relatively longstanding open question of proving time-space trade-offs for PC and CP. Namely, we exhibit a family of modified pebbling formulas {F_n} such that: - The formulas F_n have size O(n) and width O(1). - They have proofs in length O(n) in resolution, which generalize to both PC and CP. - Any refutation in CP or PCR (a generalization of PC) in length L and space s must satisfy s log L ≈ √[4]{n}. A crucial technical ingredient in these results is a new two-player communication complexity lower bound for composed search problems in terms of block sensitivity, a contribution that we believe to be of independent interest.