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The free group F S with free generating set S can be constructed as follows. S is a set of symbols, and we suppose for every s in S there is a corresponding "inverse" symbol, s −1, in a set S −1. Let T = S ∪ S −1, and define a word in S to be any written product of elements of T. That is, a word in S is an element of the monoid ...
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 of . The word problem is a well-known example of an undecidable problem .
One way of remembering this is that the word ‘noun’ comes before the word ‘verb’ in the dictionary; likewise ‘c’ comes before ‘s’, so the nouns are ‘practice, licence, advice’ and the verbs are ‘practise, license, advise’. [27] Here or Hear; We hear with our ear. Complement and Compliment; complement adds something to ...
Presentation of a group. In mathematics, a presentation is one method of specifying a group. A presentation of a group G comprises a set S of generators —so that every element of the group can be written as a product of powers of some of these generators—and a set R of relations among those generators. We then say G has presentation.
Dr. Sbaitso / ˈsbeɪtsoʊ / SBAY-tsoh / səˈb -/ / ˈzb -/ is an artificial intelligence speech synthesis program released late in 1991 [ 1] by Creative Labs in Singapore for MS-DOS -based personal computers. The name is an acronym for " S ound B laster A cting I ntelligent T ext-to- S peech O perator."
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. A deep result of computational theory is that answering this question is in many ...
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