Related papers: Unique key Horn functions

This report details the generation and use of tree node ordering keys in a single relational database table. The keys for each node are calculated from the keys of its parent, in such a way that the sort order places every node in the tree…

In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this…

We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…

We formulate and optimally solve a new generalized Set Similarity Search problem, which assumes the size of the database and query sets are known in advance. By creating polylog copies of our data-structure, we optimally solve any symmetric…

Given a simple connected undirected graph G = (V, E), a set X \subseteq V(G), and integers k and p, STEINER SUBGRAPH EXTENSION problem asks if there exists a set S \supseteq X with at most k vertices such that G[S] is p-edge-connected. This…

Hash functions are cryptographic tools, which are notably involved in integrity checking and password storage. They are of primary importance to improve the security of exchanges through the Internet. However, as security flaws have been…

Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…

Decision trees are one of the most fundamental computational models for computing Boolean functions $f : \{0, 1\}^n \mapsto \{0, 1\}$. It is well-known that the depth and size of decision trees are closely related to time and number of…

In the problem of minimal perfect hashing, we are given a size $k$ subset $\mathcal{A}$ of a universe of keys $[n] = \{1,2, \cdots, n\}$, for which we wish to construct a hash function $h: [n] \to [k]$ such that $h(\cdot)$ maps…

In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated…

In this paper, we fully answer the above question through a key algebraic condition on graph functions, called \textit{permutation compatibility}, that relates permutations of weights and features of the graph to functional constraints. We…

We present {Kanren} (read: set-Kanren), an extension to miniKanren with constraints for reasoning about sets and association lists. {Kanren} includes first-class set objects, a functionally complete family of set-theoretic constraints…

We address counting and optimization variants of multicriteria global min-cut and size-constrained min-$k$-cut in hypergraphs. 1. For an $r$-rank $n$-vertex hypergraph endowed with $t$ hyperedge-cost functions, we show that the number of…

We consider the following fundamental problems: (1) Constructing $k$-independent hash functions with a space-time tradeoff close to Siegel's lower bound. (2) Constructing representations of unbalanced expander graphs having small size and…

Sequence classification has a wide range of real-world applications in different domains, such as genome classification in health and anomaly detection in business. However, the lack of explicit features in sequence data makes it difficult…

Functional programming languages are particularly well-suited for building automated reasoning systems, since (among other reasons) a logical term is well modeled by an inductive type, traversing a term can be implemented generically as a…

Given a set $K$ of $n$ keys, a minimal perfect hash function (MPHF) is a collision-free bijective map $\mathsf{H_{mphf}}$ from $K$ to $\{0, \dots, n-1\}$. This work presents a (minimal) perfect hash function that first prioritizes query…

Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data…

Visual recognition relies on understanding the semantics of image tokens and their complex interactions. Mainstream self-attention methods, while effective at modeling global pair-wise relations, fail to capture high-order associations…

Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…