# Proof Complexity Meets Algebra

@article{Atserias2017ProofCM,
title={Proof Complexity Meets Algebra},
author={Albert Atserias and Joanna Ochremiak},
journal={ArXiv},
year={2017},
volume={abs/1711.07320}
}
• Published 20 November 2017
• Mathematics, Computer Science
• ArXiv
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of pp-interpretability, homomorphic equivalence and addition of constants to a core preserve the proof complexity of the CSP. As a result, for those proof systems, the classes of constraint languages for which small unsatisfiability certificates exist can be… Expand
12 Citations
Proof Complexity Meets Algebra
• Computer Science, Mathematics
• ACM Trans. Comput. Log.
• 2019
It is shown that, for the most studied propositional, algebraic, and semialgebraic proof systems, the classical constructions of pp-interpretability, homomorphic equivalence, and addition of constants to a core preserve the proof complexity of the CSP. Expand
A Finite-Model-Theoretic View on Propositional Proof Complexity
• Mathematics, Computer Science
• ArXiv
• 2018
This work shows that the power of several propositional proof systems, such as Horn resolution, bounded-width resolution, and the polynomial calculus of bounded degree, can be characterised in a precise sense by variants of fixed-point logics that are of fundamental importance in descriptive complexity theory. Expand
Chapter 7. Proof Complexity and SAT Solving
• Computer Science
• 2021
CNF SAT serves as the canonical hard decision problem, and is frequently conjectured to require exponential time to solve, in contrast, for practical theorem proving, CNF SAT is the core method for encoding and solving problems. Expand
Promise Constraint Satisfaction and Width
• Computer Science
• ArXiv
• 2021
The main technical finding is that the template of every PCSP that is solvable in bounded width satisfies a certain structural condition implying that its algebraic closure-properties include weak near unanimity polymorphisms of all large arities. Expand
Sailing Routes in the World of Computation
• Computer Science
• Lecture Notes in Computer Science
• 2018
The tutorial focuses on computably enumerable (c.e.) structures, a class that properly extends the class of all computable structures and the interplay between important constructions, concepts, and results in computability, universal algebra, and algebra. Expand
GROUP, GRAPHS, ALGORITHMS: THE GRAPH ISOMORPHISM PROBLEM
• L. Babai
• Computer Science
• Proceedings of the International Congress of Mathematicians (ICM 2018)
• 2019
Graph Isomorphism (GI) is one of a small number of natural algorithmic problems with unsettled complexity status in the P /NP theory: not expected to be NP-complete, yet not known to be solvable inExpand
Algorithm Analysis Through Proof Complexity
This work surveys the proof complexity literature that adopts this approach relative to two $$\mathsf {NP}$$-problems: k-clique and 3-coloring. Expand
The limits of SDP relaxations for general-valued CSPs
• Computer Science, Mathematics
• 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
• 2017
It has been shown that for a general-valued constraint language Γ the following statements are equivalent: (1) any instance of VCSP(Γ) can be solved to optimality using a constant level of theExpand
Nullstellensatz size-degree trade-offs from reversible pebbling
• Computer Science, Mathematics
• Computational Complexity Conference
• 2019
We establish an exactly tight relation between reversible pebblings of graphs and Nullstellensatz refutations of pebbling formulas, showing that a graph G can be reversibly pebbled in time t andExpand
H-coloring Dichotomy in Proof Complexity
The $\mathcal{H}$-coloring problem can be considered as an example of the computational problem from a huge class of the constraint satisfaction problems (CSP): an $\mathcal{H}$-coloring of a graphExpand

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