Search results
Results from the WOW.Com Content Network
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]
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 ...
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.
An order that is both translation-invariant and a well-order is called a reduction order. From the presentation of the monoid it is possible to define a rewriting system given by the relations R. If A x B is in R then either A < B in which case B → A is a rule in the rewriting system, otherwise A > B and A → B.
A Lyndon word is a word over a given alphabet that is written in its simplest and most ordered form out of its respective conjugacy class. Lyndon words are important because for any given Lyndon word x {\displaystyle x} , there exists Lyndon words y {\displaystyle y} and z {\displaystyle z} , with y < z {\displaystyle y<z} , x = y z ...
A Latin square of order n is an n × n array with entries from a set of n elements with the property that each element of the set occurs exactly once in each row and each column of the array. An example of a Latin square of order three is given by,
On the row beneath “Pay to the order of,” write the payment amount in words. Sign your name on the line in the bottom right. Write a brief description on the “memo” line at the bottom left ...
Given a regular expression, determining whether it generates every string over its alphabet is PSPACE-complete. [6] The first known PSPACE-complete problem was the word problem for deterministic context-sensitive grammars. In the word problem for context-sensitive grammars, one is given a set of grammatical transformations which can increase ...