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
Short proofs are narrow—resolution made simple
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Linear gaps between degrees for the polynomial calculus modulo distinct primes
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A sharp threshold in proof complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Hard examples for bounded depth frege
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On sufficient conditions for unsatisfiability of random formulas
Journal of the ACM (JACM)
Hard examples for the bounded depth Frege proof system
Computational Complexity
Lower bounds for k-DNF resolution on random 3-CNFs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Constant-depth Frege systems with counting axioms polynomially simulate Nullstellensatz refutations
ACM Transactions on Computational Logic (TOCL)
A Gröbner basis approach to CNF-formulae preprocessing
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Optimality of size-degree tradeoffs for polynomial calculus
ACM Transactions on Computational Logic (TOCL)
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
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Strong ETH holds for regular resolution
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We show a general reduction that derives lower bounds on degrees of polynomial calculus proofs of tautologies over any field of characteristic other than 2 from lower bounds for resolution proofs of a related set of linear equations modulo 2. We apply this to derive linear lower bounds on the degrees of PC proofs of randomly generated tautologies.