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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.
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. A deep result of computational theory is that answering ...
G is a word-hyperbolic group. [22] G has decidable conjugacy problem. [19] G is coherent, that is every finitely generated subgroup of G is finitely presentable. [23] The isomorphism problem is decidable for finitely generated one-relator groups with torsion, by virtue of their hyperbolicity. [24] G is residually finite. [25]
Artificial intelligence (AI), in its broadest sense, is intelligence exhibited by machines, particularly computer systems.It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. [1]
The BCH code with and higher has the generator polynomial. This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. It is also denoted as: (15, 1) BCH code. In fact, this code has only two codewords: 000000000000000 and 111111111111111 (a trivial repetition code).
An oxygen concentrator is a medical device that gives you extra oxygen. Air is made up of about 20% oxygen. An oxygen concentrator uses the air in the atmosphere, filters it, and gives you air ...
Word problem (mathematics education) 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. As most word problems involve a narrative of some sort, they are ...
Here, codeword polynomial is an element of a linear code whose code words are polynomials that are divisible by a polynomial of shorter length called the generator polynomial. Every codeword polynomial can be expressed in the form c ( x ) = a ( x ) g ( x ) {\displaystyle c(x)=a(x)g(x)} , where g ( x ) {\displaystyle g(x)} is the generator ...
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