In mathematics, a finitary relation over a sequence of sets X1, ..., Xn is a subset of the Cartesian product X1 × ... × Xn; that is, it is a set of n-tuples (x1, ..., xn), each being a sequence of elements xi in the corresponding 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.
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research focusing on the resolution of particular forms of the constraint satisfaction problem.
Computational semiotics is an interdisciplinary field that applies, conducts, and draws on research in logic, mathematics, the theory and practice of computation, formal and natural language studies, the cognitive sciences generally, and semiotics proper. The term encompasses both the application of semiotics to computer hardware and software design and, conversely, the use of computation for performing semiotic analysis. The former focuses on what semiotics can bring to computation; the latter on what computation can bring to semiotics.
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science, and more specifically the Computer Sciences, which uses advanced computing capabilities to understand and solve complex physical problems. While this typically extends into visual computation, this field of study typically includes:
Dagstuhl is a computer science research center in Germany, located in and named after a district of the town of Wadern, Merzig-Wadern, Saarland.
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 }.
In computer science, an abstract state machine (ASM) is a state machine operating on states that are arbitrary data structures.
BCS-FACS is the BCS Formal Aspects of Computing Science Specialist Group.
In mathematics, the converse 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.
Chris Brink, CBE, FRSSAf is a South African mathematician and academic. He was the Vice-Chancellor of Newcastle University between 2007 and December 2016.
The term "information algebra" refers to mathematical techniques of information processing. Classical information theory goes back to Claude Shannon. It is a theory of information transmission, looking at communication and storage. However, it has not been considered so far that information comes from different sources and that it is therefore usually combined. It has furthermore been neglected in classical information theory that one wants to extract those parts out of a piece of information that are relevant to specific questions.
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.
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.
Joseph Frederick Traub was an American computer scientist. He was the Edwin Howard Armstrong Professor of Computer Science at Columbia University and External Professor at the Santa Fe Institute. He held positions at Bell Laboratories, University of Washington, Carnegie Mellon, and Columbia, as well as sabbatical positions at Stanford, Berkeley, Princeton, California Institute of Technology, and Technical University, Munich.
Susanne Boll is a Professor for Media Informatics and Multimedia Systems in the Department of Computing Science at the University of Oldenburg, Germany. and is a member of the board at the research institute OFFIS. She is a member of SIGMM and SIGCHI of the ACM as well as the German Informatics Society GI. She founded and directs the HCI Lab at the University of Oldenburg and OFFIS.
Tomasz Imieliński is a Polish-American computer scientist, most known in the areas of data mining, mobile computing, data extraction, and search engine technology. He is currently a professor of computer science at Rutgers University in New Jersey, United States.
Gunther Schmidt is a German mathematician who works also in informatics.
Rudolf Berghammer is a German mathematician who works in computer science.
Deepak Kapur is a Distinguished Professor in the Department of Computer Science at the University of New Mexico.
