Related papers: Lower bounds for set-blocked clauses proofs

The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…

Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…

Fine-tuning pre-trained models have achieved impressive performance on standard natural language processing benchmarks. However, the resultant model generalizability remains poorly understood. We do not know, for example, how excellent…

One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…

The *algebrization barrier*, proposed by Aaronson and Wigderson (STOC '08, ToCT '09), captures the limitations of many complexity-theoretic techniques based on arithmetization. Notably, several circuit lower bounds that overcome the…

We present a detailed study of estimation errors in terms of surrogate loss estimation errors. We refer to such guarantees as $\mathscr{H}$-consistency estimation error bounds, since they account for the hypothesis set $\mathscr{H}$…

This paper extends prior work on the connections between logics from finite model theory and propositional/algebraic proof systems. We show that if all non-isomorphic graphs in a given graph class can be distinguished in the logic…

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in references [1], [6] and [5] e.g. to the projective levels.

In ASPIC-style structured argumentation an argument can rebut another argument by attacking its conclusion. Two ways of formalizing rebuttal have been proposed: In restricted rebuttal, the attacked conclusion must have been arrived at with…

In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $\mathbf{P}$ at least as strong as Full Lambek calculus, $\mathbf{FL}$, and polynomially simulated by the extended Frege…

Proving complexity lower bounds remains a challenging task: we only know how to prove conditional uniform lower bounds and nonuniform lower bounds in restricted circuit models. Williams (STOC 2010) showed how to derive nonuniform lower…

The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming…

A combinatorial principle CECA is formulated and its equivalence with GCH+ certain weakenings of Box_lambda for singular lambda is proved. CECA is used to show that certain ``almost point- < tau'' families can be refined to point- < tau…

Many recent works on Entity Resolution (ER) leverage Deep Learning techniques involving language models to improve effectiveness. This is applied to both main steps of ER, i.e., blocking and matching. Several pre-trained embeddings have…

Strong blocking sets, introduced first in 2011 in connection with saturating sets, have recently gained a lot of attention due to their correspondence with minimal codes. In this paper, we dig into the geometry of the concatenation method,…

This paper introduces the exponential substitution calculus (ESC), a new presentation of cut elimination for IMELL, based on proof terms and building on the idea that exponentials can be seen as explicit substitutions. The idea in itself is…

Answering Boolean conjunctive queries over the guarded fragment is decidable, however, as yet no practical decision procedure exists. Meanwhile, ordered resolution, as a practically oriented algorithm, is widely used in state-of-art modern…

This paper concerns Boolean satisfiability (SAT) solvers based on Ordered Binary Decision Diagrams (BDDs), especially those that can generate proofs of unsatisfiability. Mengel (arXiv:2306.00886) has presented a theoretical analysis that a…

We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…

We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that…