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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]
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.
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In computer programming, the lexer hack is a solution to parsing context-sensitive grammars such as C, where classifying a sequence of characters as a variable name or a type name requires contextual information, by feeding contextual information backwards from the parser to the lexer.
The Gettier problem, in the field of epistemology, is a landmark philosophical problem concerning the understanding of descriptive knowledge. Attributed to American philosopher Edmund Gettier , Gettier-type counterexamples (called "Gettier-cases") challenge the long-held justified true belief (JTB) account of knowledge.
A property, in some object-oriented programming languages, is a special sort of class member, intermediate in functionality between a field (or data member) and a method.The syntax for reading and writing of properties is like for fields, but property reads and writes are (usually) translated to 'getter' and 'setter' method calls.
Then the word problem in is solvable: given two words , in the generators of , write them as words in and compare them using the solution to the word problem in . It is easy to think that this demonstrates a uniform solution of the word problem for the class K {\displaystyle K} (say) of finitely generated groups that can be embedded in G ...
Generalizing the setting of the Muller–Schupp theorem, Brough [15] studied groups with poly-context-free word problem, that is where the word problem is the intersection of finitely many context-free languages. Poly-context-free groups include all finitely generated groups commensurable with groups embeddable in a direct product of finitely ...