Journal of the ACM (JACM)
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The complexity of stochastic games
Information and Computation
Discrete Applied Mathematics
Lower bounds to the size of constant-depth propositional proofs
Journal of Symbolic Logic
The complexity of mean payoff games on graphs
Theoretical Computer Science
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On Interpolation and Automatization for Frege Systems
SIAM Journal on Computing
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Linear lower bound on degrees of positivstellensatz calculus proofs for the parity
Theoretical Computer Science
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
On reducibility and symmetry of disjoint NP pairs
Theoretical Computer Science - Mathematical foundations of computer science
Optimality of size-width tradeoffs for resolution
Computational Complexity
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
On the automatizability of resolution and related propositional proof systems
Information and Computation
Hard examples for the bounded depth Frege proof system
Computational Complexity
On the complexity of resolution with bounded conjunctions
Theoretical Computer Science
Non-automatizability of bounded-depth frege proofs
Computational Complexity
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Resolution Is Not Automatizable Unless W[P] Is Tractable
SIAM Journal on Computing
Mean-payoff games and propositional proofs
Information and Computation
Clause-learning algorithms with many restarts and bounded-width resolution
Journal of Artificial Intelligence Research
Automatizability and simple stochastic games
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Hypercontractivity, sum-of-squares proofs, and their applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Exponential Lower Bounds and Integrality Gaps for Tree-Like Lovász-Schrijver Procedures
SIAM Journal on Computing
Parameterized Complexity
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In recent years there has been some progress in our understanding of the proof-search problem for very low-depth proof systems, e.g. proof systems that manipulate formulas of very low complexity such as clauses (i.e. resolution), DNF-formulas (i.e. R(k) systems), or polynomial inequalities (i.e. semi-algebraic proof systems). In this talk I will overview this progress. I will start with bounded-width resolution, whose specialized proof-search algorithm is as easy as uninteresting, but whose proof-search problem is unintentionally solved by certain versions of conflict-driven clause-learning algorithms with restarts. I will continue with R(k) systems, whose proof-search problem turned out to hide the complexity of certain two-player games of interest in the area of systems synthesis and verification. And I will close with bounded-degree semi-algebraic proof systems, whose proof-search problem turned out to hide the complexity of systems of linear equations over finite fields, among other problems.