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A Finite-Model-Theoretic View on Propositional Proof Complexity [PDF]
Logical Methods in Computer Science, 2022 We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width resolution, and the ...
Erich Grädel +3 more
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Separations in Proof Complexity and TFNP [PDF]
2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), 2022 It is well-known that Resolution proofs can be efficiently simulated by Sherali-Adams (SA) proofs. We show 1, however, that any such simulation needs to exploit huge coefficients: Resolution cannot be efficiently simulated by SA when the coefficients are
Mika Göös +6 more
semanticscholar +6 more sources
On the relative proof complexity of deep inference via atomic flows [PDF]
Logical Methods in Computer Science, 2015 We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore ...
Anupam Das
doaj +3 more sources
Circuit Complexity, Proof Complexity, and Polynomial Identity Testing [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2014 We introduce a new and natural algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent ...
Toniann Pitassi
exaly +2 more sources
On the algebraic proof complexity of Tensor Isomorphism [PDF]
Cybersecurity and Cyberforensics Conference, 2023 The Tensor Isomorphism problem (TI) has recently emerged as having connections to multiple areas of research within complexity and beyond, but the current best upper bound is essentially the brute force algorithm.
Nicola Galesi +3 more
semanticscholar +1 more source
ON THE EXISTENCE OF STRONG PROOF COMPLEXITY GENERATORS [PDF]
Bulletin of Symbolic Logic, 2022 Cook and Reckhow [5] pointed out that $\mathcal {N}\mathcal {P} \neq co\mathcal {N}\mathcal {P}$ iff there is no propositional proof system that admits polynomial size proofs of all tautologies.
J. Krajícek
semanticscholar +1 more source
Annals of Pure and Applied Logic, 2022 The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.
Azza Gaysin
semanticscholar +1 more source
Pebble Games, Proof Complexity, and Time-Space Trade-offs [PDF]
Logical Methods in Computer Science, 2013 Pebble games were extensively studied in the 1970s and 1980s in a number of different contexts. The last decade has seen a revival of interest in pebble games coming from the field of proof complexity. Pebbling has proven to be a useful tool for studying
Jakob Nordstrom
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Sublogarithmic uniform Boolean proof nets [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 Using a proofs-as-programs correspondence, Terui was able to compare two models of parallel computation: Boolean circuits and proof nets for multiplicative linear logic. Mogbil et. al.
Clément Aubert
doaj +1 more source
Gravitation from optimized computation: Einstein and beyond
Journal of High Energy Physics, 2023 A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics.
Rafael Carrasco +3 more
doaj +1 more source