Search results
Results from the WOW.Com Content Network
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.
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.
The Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix [1]) is a semi-decision [2] [3] algorithm for transforming a set of equations (over terms) into a confluent term rewriting system. When the algorithm succeeds, it effectively solves the word problem for the specified algebra.
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 ...
In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2]
The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do. The set of NP-complete problems is often denoted by NP-C or NPC. Although a solution to an NP-complete problem can be verified "quickly", there is no known way to find a solution quickly.
Many word problems are undecidable based on the Post correspondence problem. Any two homomorphisms, with a common domain and a common codomain form an instance of the Post correspondence problem, which asks whether there exists a word in the domain such that () = (). Post proved that this problem is undecidable; consequently, any word problem ...
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Donate; Help; Learn to edit; Community portal; Recent changes; Upload file