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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
For this problem, we are typically given a list of words and associated word senses, e.g. from a dictionary or from an online resource such as WordNet. Word-sense induction – open problem of natural-language processing, which concerns the automatic identification of the senses of a word (i.e. meanings). Given that the output of word-sense ...
But there's no way to group two English words producing a single French word. An example of a word-based translation system is the freely available GIZA++ package , which includes the training program for IBM models and HMM model and Model 6. [7] The word-based translation is not widely used today; phrase-based systems are more common.
An algebraic expression is an expression built up from algebraic constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by a rational number). [41] For example, 3x 2 − 2xy + c is an algebraic expression.
It is used in natural language processing and information retrieval (IR). It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a ...
Word Processing in Groups is a monograph in mathematics on the theory of automatic groups, a type of abstract algebra whose operations are defined by the behavior of finite automata. The book's authors are David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Mike Paterson, and William Thurston.
For other problems, such as the 5th, experts have traditionally agreed on a single interpretation, and a solution to the accepted interpretation has been given, but closely related unsolved problems exist. Some of Hilbert's statements were not precise enough to specify a particular problem, but were suggestive enough that certain problems of ...