Related papers: Exponential Lower Bounds and Separation for Query …
This paper investigates linear programming based branch-and-bound using general disjunctions, also known as stabbing planes, for solving integer programs. We derive the first sub-exponential lower bound (in the encoding length $L$ of the…
We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…
Evaluating whether large language models (LLMs) capture the structure of natural language beyond local fluency remains an open challenge. Existing evaluation methods, largely based on task performance or short-context behavior, provide…
We exhibit a monotone function computable by a monotone circuit of quasipolynomial size such that any monotone circuit of polynomial depth requires exponential size. This is the first size-depth tradeoff result for monotone circuits in the…
In ontology-based data access (OBDA), ontologies have been successfully employed for querying possibly unstructured and incomplete data. In this paper, we advocate using ontologies not only to formulate queries and compute their answers,…
We study the problem of finite entailment of ontology-mediated queries. Going beyond local queries, we allow transitive closure over roles. We focus on ontologies formulated in the description logics ALCOI and ALCOQ, extended with…
Verification of properties of first order logic with two variables FO2 has been investigated in a number of contexts. Over arbitrary structures it is known to be decidable with NEXPTIME complexity, with finitely satisfiable formulas having…
We study the power of negation in the Boolean and algebraic settings and show the following results. * We construct a family of polynomials $P_n$ in $n$ variables, all of whose monomials have positive coefficients, such that $P_n$ can be…
Ontology-based data access is an approach to organizing access to a database augmented with a logical theory. In this approach query answering proceeds through a reformulation of a given query into a new one which can be answered without…
The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential…
We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recurrent words $w$ whose complexity functions $p_w(n)$ are…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
Recent advancements in large language models (LLMs) have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling…
Exponential parallelism, a defining principle of advanced computational systems, holds promise for transformative impacts across several scientific and industrial domains. This feature paper provides a comparative overview of Quantum…
We show that the reciprocal of a partial sum with 2m terms of the alternating exponential series is the exponential generating function for permutations in which every increasing run has length congruent to 0 or 1 modulo 2m. More generally…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
We prove the first unconditional consistency result for superpolynomial circuit lower bounds with a relatively strong theory of bounded arithmetic. Namely, we show that the theory V$^0_2$ is consistent with the conjecture that NEXP…
In this paper, we consider first-order logic over unary functions and study the complexity of the evaluation problem for conjunctive queries described by such kind of formulas. A natural notion of query acyclicity for this language is…
The design of machines and algorithms capable of learning in a dynamically changing environment has become an increasingly topical problem with the increase of the size and heterogeneity of data available to learning systems. As a…
While it is known that there is at most a polynomial separation between quantum query complexity and the polynomial degree for total functions, the precise relationship between the two is not clear for partial functions. In this paper, we…