Journal of the ACM (JACM)
Many hard examples for resolution
Journal of the ACM (JACM)
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
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
Linear gaps between degrees for the polynomial calculus modulo distinct primes
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Information and Computation
Space Complexity in Propositional Calculus
SIAM Journal on Computing
Resolution lower bounds for the weak functional pigeonhole principle
Theoretical Computer Science - Logic and complexity in computer science
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Space complexity of random formulae in resolution
Random Structures & Algorithms
Resolution lower bounds for the weak pigeonhole principle
Journal of the ACM (JACM)
A combinatorial characterization of resolution width
Journal of Computer and System Sciences
Linear Level Lasserre Lower Bounds for Certain k-CSPs
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
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
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
A simplified way of proving trade-off results for resolution
Information Processing Letters
Size-Space Tradeoffs for Resolution
SIAM Journal on Computing
Storage requirements for deterministic polynomialtime recognizable languages
Journal of Computer and System Sciences
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
Toward a Model for Backtracking and Dynamic Programming
Computational Complexity - Special issue in memory of Misha Alekhnovich
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
Space Complexity in Polynomial Calculus
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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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We present size-space trade-offs for the polynomial calculus (PC) and polynomial calculus resolution (PCR) proof systems. These are the first true size-space trade-offs in any algebraic proof system, showing that size and space cannot be simultaneously optimized in these models. We achieve this by extending essentially all known size-space trade-offs for resolution to PC and PCR. As such, our results cover space complexity from constant all the way up to exponential and yield mostly superpolynomial or even exponential size blow-ups. Since the upper bounds in our trade-offs hold for resolution, our work shows that there are formulas for which adding algebraic reasoning on top of resolution does not improve the trade-off properties in any significant way. As byproducts of our analysis, we also obtain trade-offs between space and degree in PC and PCR exactly matching analogous results for space versus width in resolution, and strengthen the resolution trade-offs in [Beame, Beck, and Impagliazzo '12] to apply also to k-CNF formulas.