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Publication# Succinct ordering and aggregation constraints in algebraic array theories

Abstract

We discuss two extensions to a recently introduced theory of arrays, which are based on considerations coming from the model theory of power structures. First, we discuss how the ordering relation on the index set can be expressed succinctly by referring to arbitrary Venn regions. Second, we show how to add general aggregators to the calculus. The result is a logic that subsumes four previous fragments discussed in the literature and is distinct from array fold logic, in that it can express summations, while its satisfiability problem remains in non -deterministic polynomial time.

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Related concepts (38)

Related publications (35)

Model theory

In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself.

Binary relation

In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets X and Y is a new set of ordered pairs (x, y) consisting of elements x in X and y in Y. It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element x is related to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation.

Connected relation

In mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all pairs of elements of the set in one direction or the other while it is called strongly connected if it relates pairs of elements. As described in the terminology section below, the terminology for these properties is not uniform. This notion of "total" should not be confused with that of a total relation in the sense that for all there is a so that (see serial relation).

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