Related papers: Smoothing the gap between NP and ER
Entity resolution (ER) aims at matching records that refer to the same real-world entity. Although widely studied for the last 50 years, ER still represents a challenging data management problem, and several recent works have started to…
A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…
The Exact Matching (EM) problem asks whether there exists a perfect matching which uses a prescribed number of red edges in a red/blue edge-colored graph. While there exists a randomized polynomial-time algorithm for the problem, only some…
Autonomous systems increasingly operate under partial observability where execution-relevant state is never fully accessible. Existing governance mechanisms -- trusted execution environments, oracle-signed state proofs, cryptographic…
Accurate and efficient entity resolution (ER) has been a problem in data analysis and data mining projects for decades. In our work, we are interested in developing ER methods to handle big data. Good public datasets are restricted in this…
Entity Resolution (ER) is the task of finding entity profiles that correspond to the same real-world entity. Progressive ER aims to efficiently resolve large datasets when limited time and/or computational resources are available. In…
We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the…
Benjelloun et al. \cite{BGSWW} considered the Entity Resolution (ER) problem as the generic process of matching and merging entity records judged to represent the same real world object. They treated the functions for matching and merging…
Descriptive complexity theory aims at inferring a problem's computational complexity from the syntactic complexity of its description. A cornerstone of this theory is Fagin's Theorem, by which a graph property is expressible in existential…
We study a basic algorithmic problem in algebraic geometry, which we call NNL, of constructing a normalizing map as per Noether's Normalization Lemma. For general explicit varieties, as formally defined in this paper, we give a randomized…
Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…
The complexity class $\exists\mathbb R$, standing for the complexity of deciding the existential first order theory of the reals as real closed field in the Turing model, has raised considerable interest in recent years. It is well known…
Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classical problem in computational…
Smoothing classifiers and probability density functions with Gaussian kernels appear unrelated, but in this work, they are unified for the problem of robust classification. The key building block is approximating the $\textit{energy…
We prove new hardness results for fundamental lattice problems under the Exponential Time Hypothesis (ETH). Building on a recent breakthrough by Bitansky et al.\ \cite{BHIRW24}, who gave a polynomial-time reduction from $\mathsf{3SAT}$ to…
The diversity and Zipfian frequency distribution of natural language predicates in corpora leads to sparsity in Entailment Graphs (EGs) built by Open Relation Extraction (ORE). EGs are computationally efficient and explainable models of…
One of the fundamental open questions in computational complexity is whether the class of problems solvable by use of stochasticity under the Random Polynomial time (RP) model is larger than the class of those solvable in deterministic…
As neural networks (NNs) are increasingly introduced into safety-critical domains, there is a growing need to formally verify NNs before deployment. In this work we focus on the formal verification problem of NN equivalence which aims to…
Theorem proving is fundamental to program verification, where the automated proof of Verification Conditions (VCs) remains a primary bottleneck. Real-world program verification frequently encounters hard VCs that existing Automated Theorem…