Related papers: Consistency of Relations over Monoids

Since the early days of relational databases, it was realized that acyclic hypergraphs give rise to database schemas with desirable structural and algorithmic properties. In a by-now classical paper, Beeri, Fagin, Maier, and Yannakakis…

In several different settings, one comes across situations in which the objects of study are locally consistent but globally inconsistent. Earlier work about probability distributions by Vorob'ev (1962) and about database relations by…

Local consistency arises in diverse areas, including Bayesian statistics, relational databases, and quantum foundations, and so does the notion of functional dependence. We adopt a general approach to study logical inference in a setting…

During the early days of relational database theory it was realized that "acyclic" database schemas possess a number of desirable semantic properties. In fact, three different notions of "acyclicity" were identified and extensively…

We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…

We introduce the concept of parity symmetry in restricted spatial domains -- local parity -- and explore its impact on the stationary transport properties of generic, one-dimensional aperiodic potentials of compact support. It is shown…

This paper investigates the interplay between local and global equivalences on noncommutative polynomials, the elements of the free algebra. When the latter are viewed as functions in several matrix variables, a local equivalence of…

The semijoin operation is a fundamental operation of relational algebra that has been extensively used in query processing. Furthermore, semijoins have been used to formulate desirable properties of acyclic schemas; in particular, a schema…

In this paper, we show that the presence of the Archimedean and the mixture-continuity properties of a binary relation, both empirically non-falsifiable in principle, foreclose the possibility of consistency (transitivity) without…

A conjunctive query (CQ) is semantically acyclic if it is equivalent to an acyclic one. Semantic acyclicity has been studied in the constraint-free case, and deciding whether a query enjoys this property is NP-complete. However, in case the…

A matching queue is described via a graph $G$ together with a matching policy. Specifically, to each node in the graph there is a corresponding arrival process of items which can either be queued, or matched with queued items in neighboring…

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…

In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to…

Consider a commutative monoid $(M,+,0)$ and a biadditive binary operation $\mu \colon M \times M \to M$. We will show that under some additional general assumptions, the operation $\mu$ is automatically both associative and commutative. The…

In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…

A relation consisting of tuples annotated by an element of a monoid K is called a K-relation. A K-database is a collection of K-relations. In this paper, we study entailment of inclusion dependencies over K-databases, where K is a positive…

Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms…

The cyclic shift graph of a monoid is the graph whose vertices are the elements of the monoid and whose edges connect elements that are cyclic shift related. The Patience Sorting algorithm admits two generalizations to words, from which two…

Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…

Distributed storage systems and databases are widely used by various types of applications. Transactional access to these storage systems is an important abstraction allowing application programmers to consider blocks of actions (i.e.,…