Formal Definition
Hopcroft and Ullman (1979, p. 148) formally define a (one-tape) Turing machine as a 7-tuple where
- is a finite, non-empty set of states
- is a finite, non-empty set of the tape alphabet/symbols
- is the blank symbol (the only symbol allowed to occur on the tape infinitely often at any step during the computation)
- is the set of input symbols
- is the initial state
- is the set of final or accepting states.
- is a partial function called the transition function, where L is left shift, R is right shift. (A relatively uncommon variant allows "no shift", say N, as a third element of the latter set.)
Anything that operates according to these specifications is a Turing machine.
The 7-tuple for the 3-state busy beaver looks like this (see more about this busy beaver at Turing machine examples):
- ("blank")
- (the initial state)
- see state-table below
Initially all tape cells are marked with 0.
Tape symbol | Current state A | Current state B | Current state C | ||||||
---|---|---|---|---|---|---|---|---|---|
Write symbol | Move tape | Next state | Write symbol | Move tape | Next state | Write symbol | Move tape | Next state | |
0 | 1 | R | B | 1 | L | A | 1 | L | B |
1 | 1 | L | C | 1 | R | B | 1 | R | HALT |
Read more about this topic: Turing Machine
Famous quotes containing the words formal and/or definition:
“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prizedall these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animalsjust as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)