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e. In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant. [1] In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a certain class of possible functions.
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms.
For example, in statistical parsing a dynamic programming algorithm can be used to discover the single most likely context-free derivation (parse) of a string, which is commonly called the "Viterbi parse". [4] [5] [6] Another application is in target tracking, where the track is computed that assigns a maximum likelihood to a sequence of ...
Computational group theory. In mathematics, computational group theory is the study of groups by means of computers. It is concerned with designing and analysing algorithms and data structures to compute information about groups. The subject has attracted interest because for many interesting groups (including most of the sporadic groups) it is ...
The missionaries and cannibals problem, and the closely related jealous husbands problem, are classic river-crossing logic puzzles. [1] The missionaries and cannibals problem is a well-known toy problem in artificial intelligence, where it was used by Saul Amarel as an example of problem representation. [2][3]
Gale–Shapley algorithm. In mathematics, economics, and computer science, the Gale–Shapley algorithm (also known as the deferred acceptance algorithm, [1] propose-and-reject algorithm, [2] or Boston Pool algorithm[1]) is an algorithm for finding a solution to the stable matching problem. It is named for David Gale and Lloyd Shapley, who ...
Constraint satisfaction. In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. [1] A solution is therefore an assignment of values to the variables that satisfies all constraints—that is, a point in ...
Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields.