Combinatorica
Proceedings of the first Malta conference on Graphs and combinatorics
Exponential lower bounds for the pigeonhole principle
Computational Complexity
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
An exponential lower bound to the size of bounded depth Frege proofs of the Pigeonhole Principle
Random Structures & Algorithms
Proof complexity in algebraic systems and bounded depth Frege systems with modular counting
Computational Complexity
Lower bounds for the polynomial calculus and the Gröbner basis algorithm
Computational Complexity
Lower bounds for the polynomial calculus
Computational Complexity
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
Complexity of Positivstellensatz proofs for the knapsack
Computational Complexity
Affine Projections of Symmetric Polynomials
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Lower Bounds for Polynomial Calculus: Non-Binomial Case
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Exponential lower bounds and integrality gaps for tree-like Lovász-Schrijver procedures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Algebraic proofs over noncommutative formulas
Information and Computation
Algebraic proofs over noncommutative formulas
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
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We introduce two algebraic propositional proof systems F-NS and F-PC. The main difference of our systems from (customary) Nullstellensatz and polynomial calculus is that the polynomials are represented as arbitrary formulas (rather than sums of monomials). Short proofs of Tseitin's tautologies in the constant-depth version of F-NS provide an exponential separation between this system and Polynomial Calculus.We prove that F-NS (and hence F-PC) polynomially simulates Frege systems, and that the constant-depth version of F-PC over finite field polynomially simulates constant-depth Frege systems with modular counting. We also present a short constant-depth F-PC (in fact, F-NS) proof of the propositional pigeon-hole principle. Finally, we introduce several extensions of our systems and pose numerous open questions.