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Word problem (mathematics) In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
Word problem for groups. In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group is the algorithmic problem of deciding whether two words in the generators represent the same element. The word problem is a well-known example of an undecidable problem .
G is a word-hyperbolic group. G has decidable conjugacy problem. G is coherent, that is every finitely generated subgroup of G is finitely presentable. The isomorphism problem is decidable for finitely generated one-relator groups with torsion, by virtue of their hyperbolicity. G is residually finite. Magnus–Moldavansky method
Hyperbolic groups have a solvable word problem. They are biautomatic and automatic. Indeed, they are strongly geodesically automatic, that is, there is an automatic structure on the group, where the language accepted by the word acceptor is the set of all geodesic words.
Dice are an example of a mechanical hardware random number generator. When a cubical die is rolled, a random number from 1 to 6 is obtained. Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated.
e. Word2vec is a technique in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a large corpus. Once trained, such a model can detect synonymous ...
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