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42 relations: Algorithm, Aperiodic semigroup, Artificial intelligence, Automata theory, Biology, Bit, Cambridge University Press, Category theory, Complexity, Composition series, Computer algebra system, Computer science, Conference on Implementation and Application of Automata, Deterministic finite automaton, Field (mathematics), Finite-state machine, Flip-flop (electronics), Game theory, GAP (computer algebra system), Green's relations, Harvard University, Homomorphism, Integer, John Rhodes (mathematician), John Wiley & Sons, Lecture Notes in Computer Science, List of finite simple groups, Massachusetts Institute of Technology, Mathematics, Matrix (mathematics), Morris Hirsch, Multiplication table, Physics, Psychology, Semigroup, Semigroup action, Semigroup with three elements, Simple group, Subgroup, Transformation semigroup, Triviality (mathematics), Wreath product.
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
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Aperiodic semigroup
In mathematics, an aperiodic semigroup is a semigroup S such that every element x ∈ S is aperiodic, that is, for each x there exists a positive integer n such that xn.
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Artificial intelligence
Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals.
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Automata theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.
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Biology
Biology is the natural science that studies life and living organisms, including their physical structure, chemical composition, function, development and evolution.
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Bit
The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Complexity
Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.
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Composition series
In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces.
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Computer algebra system
A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
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Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
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Conference on Implementation and Application of Automata
CIAA, the International Conference on Implementation and Application of Automata is an annual academic conference in the field of computer science.
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Deterministic finite automaton
In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as a deterministic finite acceptor (DFA) and a deterministic finite state machine (DFSM) or a deterministic finite state automaton (DFSA)—is a finite-state machine that accepts or rejects strings of symbols and only produces a unique computation (or run) of the automaton for each input string.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Finite-state machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation.
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Flip-flop (electronics)
In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information.
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Game theory
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".
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GAP (computer algebra system)
GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra with particular emphasis on computational group theory.
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Green's relations
In mathematics, Green's relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate.
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Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts.
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Homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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John Rhodes (mathematician)
John Lewis Rhodes is a mathematician known for work in the theory of semigroups, finite state automata, and algebraic approaches to differential equations. He was born in Columbus, Ohio, on July 16, 1937, but grew up in Wooster, Ohio, where he founded the Wooster Rocket Society as a teenager. In the fall of 1955, Rhodes entered Massachusetts Institute of Technology intending to major in physics, but he soon switched to mathematics, earning his B.S. in 1960 and his Ph.D. in 1962. His Ph.D. thesis, co-written with a graduate student from Harvard, Kenneth Krohn, became known as the Prime Decomposition Theorem, or more simply Krohn–Rhodes theory. After a year on an NSF fellowship in Paris, France, he became a member of the Faculty of Mathematics at the University of California, Berkeley, where he spent his entire teaching career. In the late 1960s Rhodes wrote The Wild Book, which quickly became an underground classic, but remained in typescript until its revision and editing by Chrystopher L. Nehaniv in 2009. The following year Springer Monographs in Mathematics published his and Benjamin Steinberg's magnum opus,, a compendium of the history of the field, but more importantly the fruit of eight years' development of finite semigroup theory. In recent years Rhodes has expanded his research, bringing the insights of semigroups into matroid theory. In 2015 he published, with Pedro V. Silva, the results of his current work in another monograph with Springer: Boolean Representations of Simplicial Complexes and Matroids.
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John Wiley & Sons
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
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Lecture Notes in Computer Science
Springer Lecture Notes in Computer Science (LNCS) is a series of computer science books published by Springer Science+Business Media (formerly Springer-Verlag) since 1973.
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List of finite simple groups
In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups.
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Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private research university located in Cambridge, Massachusetts, United States.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Morris Hirsch
Morris William Hirsch (born June 28, 1933) is an American mathematician, formerly at the University of California, Berkeley.
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Multiplication table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Psychology
Psychology is the science of behavior and mind, including conscious and unconscious phenomena, as well as feeling and thought.
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Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
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Semigroup action
In algebra and theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such a way that the product of two elements of the semigroup (using the semigroup operation) is associated with the composite of the two corresponding transformations.
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Semigroup with three elements
In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them.
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Simple group
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself.
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Subgroup
In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗.
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Transformation semigroup
In algebra, a transformation semigroup (or composition semigroup) is a collection of functions from a set to itself that is closed under function composition.
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Triviality (mathematics)
In mathematics, the adjective trivial is frequently used for objects (for example, groups or topological spaces) that have a very simple structure.
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Wreath product
In mathematics, the wreath product of group theory is a specialized product of two groups, based on a semidirect product.
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References
[1] https://en.wikipedia.org/wiki/Krohn–Rhodes_theory
