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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. A binary relation is the most studied special case n = 2 of an n-ary relation over sets X1, ..., Xn, which is a subset of the Cartesian product
In mathematics, a finitary relation over sets X1, ..., Xn is a subset of the Cartesian product X1 × ⋯ × Xn; that is, it is a set of n-tuples (x1, ..., xn) consisting of elements xi in Xi. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of 3-tuples such that when substituted to x, y and z, respectively, make the sentence true.
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification. This is typically associated with hardware or software systems, where the specification contains liveness requirements as well as safety requirements.
In mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total if the source set X equals the domain {x : there is a y with xRy }. Conversely, R is called right total if Y equals the range {y : there is an x with xRy }.
Friedrich Ludwig "Fritz" Bauer was a German pioneer of computer science and professor at the Technical University of Munich.
Unifying Theories of Programming (UTP) in computer science deals with program semantics. It shows how denotational semantics, operational semantics and algebraic semantics can be combined in a unified framework for the formal specification, design and implementation of programs and computer systems.
In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation,
In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation algebra is the algebra 2 X 2 of all binary relations on a set X, that is, subsets of the cartesian square X2, with R•S interpreted as the usual composition of binary relations R and S, and with the converse of R as the converse relation.
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R; S from two given binary relations R and S. In the calculus of relations, the composition of relations is called relative multiplication, and its result is called a relative product. Function composition is the special case of composition of relations where all relations involved are functions.
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In mathematics, a binary relation on a set may, or may not, hold between two given set members. For example, "is less than" is a relation on the set of natural numbers; it holds e.g. between 1 and 3, and likewise between 3 and 4, but neither between 3 and 1 nor between 4 and 4. As another example, "is sister of" is a relation on the set of all people, it holds e.g. between Marie Curie and Bronisława Dłuska, and likewise vice versa. Set members may not be in relation "to a certain degree" - either they are in relation or they are not.
Roland Carl Backhouse is a British computer scientist and mathematician. As of 2020, he is Emeritus Professor of Computing Science at the University of Nottingham.
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In mathematics, a rational monoid is a monoid, an algebraic structure, for which each element can be represented in a "normal form" that can be computed by a finite transducer: multiplication in such a monoid is "easy", in the sense that it can be described by a rational function.
Gunther Schmidt is a German mathematician who works also in informatics.
RAMiCS, the International Conference on Relational and Algebraic Methods in Computer Science, is an academic conference organized every eighteen months by an international steering committee and held in different locations mainly in Europe, but also in other continents. Like most theoretical computer science conferences, its contributions are strongly peer-reviewed. Proceedings of the conferences appear in Lecture Notes in Computer Science, and some of the stronger papers have been published in Journal of Logical and Algebraic Methods in Programming.
Feature engineering or feature extraction or feature discovery is the process of extracting features from raw data. Due to deep learning networks, such as convolutional neural networks, that are able to learn it by itself, domain-specific- based feature engineering has become obsolete for vision and speech processing.
References
- ↑ R. Berghammer, Gunther Schmidt, Michael Winter (2019) "Cryptomorphic topological structures: a computational relation algebraic approach", Journal of Logical and Algebraic Methods in Programming 102: 17–45, doi : 10.1016/j.jlamp.2018.09.004
