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The Riis Complexity Gap for QBF Resolution (2024)
Journal Article
Beyersdorff, O., Clymo, J., Dantchev, S., & Martin, B. (2024). The Riis Complexity Gap for QBF Resolution. Journal on Satisfiability, Boolean Modeling and Computation, 15(1), 9-25. https://doi.org/10.3233/sat-231505

We give an analogue of the Riis Complexity Gap Theorem in Resolution for Quantified Boolean Formulas (QBFs). Every first-order sentence ϕ without finite models gives rise to a sequence of QBFs whose minimal refutations in tree-like QBF Resolution sys... Read More about The Riis Complexity Gap for QBF Resolution.

Depth lower bounds in Stabbing Planes for combinatorial principles (2024)
Journal Article
Dantchev, S., Galesi, N., Ghani, A., & Martin, B. (2024). Depth lower bounds in Stabbing Planes for combinatorial principles. Logical Methods in Computer Science, 20(1), 1-19. https://doi.org/10.46298/lmcs-20%281%3A1%292024

Stabbing Planes (also known as Branch and Cut) is a proof system introduced very recently which, informally speaking, extends the DPLL method by branching on integer linear inequalities instead of single variables. The techniques known so far to prov... Read More about Depth lower bounds in Stabbing Planes for combinatorial principles.

Sherali-Adams and the binary encoding of combinatorial principles (2020)
Presentation / Conference Contribution
Dantchev, S., Ghani, A., & Martin, B. (2020, May). Sherali-Adams and the binary encoding of combinatorial principles. Presented at LATIN 2020, São Paulo, Brazil

We consider the Sherali-Adams ( SA ) refutation system together with the unusual binary encoding of certain combinatorial principles. For the unary encoding of the Pigeonhole Principle and the Least Number Principle, it is known that linear rank is r... Read More about Sherali-Adams and the binary encoding of combinatorial principles.

Resolution and the binary encoding of combinatorial principles (2019)
Presentation / Conference Contribution
Dantchev, S., Galesi, N., & Martin, B. (2019, July). Resolution and the binary encoding of combinatorial principles. Presented at Computational Complexity Conference, New Brunswick, New Jersey, USA

Res(s) is an extension of Resolution working on s-DNFs. We prove tight n (k) lower bounds for the size of refutations of the binary version of the k-Clique Principle in Res(o(log log n)). Our result improves that of Lauria, Pudlák et al. [27] who pro... Read More about Resolution and the binary encoding of combinatorial principles.

Simplicial Complex Entropy (2017)
Presentation / Conference Contribution
Dantchev, S., & Ivrissimtzis, I. (2016, June). Simplicial Complex Entropy. Presented at 9th International Conference on Mathematical Methods for Curves and Surfaces, Tønsberg, Norway

We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We focus on the com... Read More about Simplicial Complex Entropy.

Relativization makes contradictions harder for Resolution (2013)
Journal Article
Dantchev, S., & Martin, B. (2014). Relativization makes contradictions harder for Resolution. Annals of Pure and Applied Logic, 165(3), 837-857. https://doi.org/10.1016/j.apal.2013.10.009

We provide a number of simplified and improved separations between pairs of Resolution-with-bounded-conjunction refutation systems, Res(d), as well as their tree-like versions, Res∗(d). The contradictions we use are natural combinatorial principles:... Read More about Relativization makes contradictions harder for Resolution.

Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems (2012)
Journal Article
Dantchev, S., & Martin, B. (2013). Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems. Computational Complexity, 22(1), 191-213. https://doi.org/10.1007/s00037-012-0049-1

We prove a dichotomy theorem for the rank of propositional contradictions, uniformly generated from first-order sentences, in both the Lovász-Schrijver (LS) and Sherali-Adams (SA) refutation systems. More precisely, we first show that the proposition... Read More about Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems.

Cutting Planes and the Parameter Cutwidth (2012)
Journal Article
Dantchev, S., & Martin, B. (2012). Cutting Planes and the Parameter Cutwidth. Theory of Computing Systems, 51(1), 50-64. https://doi.org/10.1007/s00224-011-9373-0

We introduce the parameter cutwidth for the Cutting Planes (CP) system of Gomory and Chvátal. We provide linear lower bounds on cutwidth for two simple polytopes. Considering CP as a propositional refutation system, one can see that the cutwidth of a... Read More about Cutting Planes and the Parameter Cutwidth.