The Word Problem For Semi-Thue Systems
The word problem for semi-Thue systems can be stated as follows: Given a semi-Thue system and two words, can be transformed into by applying rules from ? This problem is undecidable, i.e. there is no general algorithm for solving this problem. This even holds if we limit the input to finite systems.
Martin Davis offers the lay reader a two-page proof in his article "What is a Computation?" pp. 258–259 with commentary p. 257. Davis casts the proof in this manner: "Invent whose solution would lead to a solution to the halting problem."
Read more about this topic: Semi-Thue System
Famous quotes containing the words word, problem and/or systems:
“You were created of your name, the word
Is that of which you were the personage.
There is no life except in the word of it.”
—Wallace Stevens (1879–1955)
“How much atonement is enough? The bombing must be allowed as at least part-payment: those of our young people who are concerned about the moral problem posed by the Allied air offensive should at least consider the moral problem that would have been posed if the German civilian population had not suffered at all.”
—Clive James (b. 1939)
“What avails it that you are a Christian, if you are not purer than the heathen, if you deny yourself no more, if you are not more religious? I know of many systems of religion esteemed heathenish whose precepts fill the reader with shame, and provoke him to new endeavors, though it be to the performance of rites merely.”
—Henry David Thoreau (1817–1862)