Related papers: Circuit Treewidth, Sentential Decision, and Query …
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables,…
Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow…
Biclustering, the process of simultaneously clustering the rows and columns of a data matrix, is a popular and effective tool for finding structure in a high-dimensional dataset. Many biclustering procedures appear to work well in practice,…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
For any Boolean functions $f$ and $g$, the question whether $R(f\circ g) = \tilde{\Theta}(R(f)R(g))$, is known as the composition question for the randomized query complexity. Similarly, the composition question for the approximate degree…
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…
We propose unifying techniques from probabilistic databases and relational embedding models with the goal of performing complex queries on incomplete and uncertain data. We formalize a probabilistic database model with respect to which all…
The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…
Counting the number of models of a Boolean formula is a fundamental problem in artificial intelligence and reasoning. Minimal models of a Boolean formula are critical in various reasoning systems, making the counting of minimal models…
Frequent tree mining asks us to enumerate tree patterns that occur frequently in a database of rooted trees. This problem is motivated by tree-structured data in bioinformatics, such as glycans and pseudoknot-free RNA secondary structures.…
We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the…
Probabilistic circuits (PCs) are models that allow exact and tractable probabilistic inference. In contrast to neural networks, they are often assumed to be well-calibrated and robust to out-of-distribution (OOD) data. In this paper, we…
We show conflict complexity of every total Boolean function, recently introduced in [Swagato Sanyal. A composition theorem via conict complexity. arXiv preprint arXiv:1801.03285, 2018.] to prove a composition theorem of randomized decision…
The proliferation of contextualized knowledge in the Semantic Web (SW) has led to the popularity of knowledge formats such as \emph{quads} in the SW community. A quad is an extension of an RDF triple with contextual information of the…
Database query engines use pull-based or push-based approaches to avoid the materialization of data across query operators. In this paper, we study these two types of query engines in depth and present the limitations and advantages of each…
Recent work on weighted model counting has been very successfully applied to the problem of probabilistic inference in Bayesian networks. The probability distribution is encoded into a Boolean normal form and compiled to a target language,…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
Despite much work within the last decade on foundational properties of SPARQL - the standard query language for RDF data - rather little is known about the exact limits of tractability for this language. In particular, this is the case for…
Traditional database queries follow a simple model: they define constraints that each tuple in the result must satisfy. This model is computationally efficient, as the database system can evaluate the query conditions on each tuple…