In mathematics, a **transition function** has several different meanings:

- In topology and in particular in the theory of manifolds, a transition function between two charts of an atlas is a map which allows to pass from one chart to the other in the region where they intersect.

- In computing, a
**transition function**is the function that defines the state transitions of a Turing machine, finite-state machine, or cellular automaton.

- In statistics and probability theory, a
**transition function**is a stochastic kernel, the conditional probability distribution function controlling the transitions of a stochastic process.

### Other articles related to "function, transition function":

... a finite set of states is the initial state is the time advanced

**function**which defines the lifespan of a state where is the set of non-negative ... is the external

**transition function**which defines how an input event changes a state of the system ... is the output and internal

**transition function**where and denotes the silent event ...

... automaton corresponds to the equivalence class containing the empty string, and the

**transition function**from a state X on input symbol y takes the ... The definition of the Myhill–Nerode relation implies that the

**transition function**is well-defined no matter which representative string x is chosen for state X, the same

**transition function**value will result ...

... state is the set of final states is the initial stack symbol is the

**transition function**, where are finite subsets of ... Thus the

**transition function**takes a state, the next symbol of the input string, and the top symbol of the current stack and generates the next state, the stacks to be pushed and popped onto the ... Such accepted strings are elements of the language where and defines the

**transition function**applied over as many times as necessary to parse the ...

... The machine's

**transition function**takes two inputs the current non-Halt state, the symbol in the current tape cell, and produces three outputs a symbol to write over the ... The

**transition function**may be seen as a finite table of 5-tuples, each of the form (current state, current symbol, symbol to write, direction of shift, next state) ... with the current tape cell being any cell of a blank (all-0) tape, and then iterating the

**transition function**until the Halt state is entered (if ever) ...

### Famous quotes containing the words function and/or transition:

“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its *function* in psychic life. It domesticates self-doubt.”

—Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)

“When I was going through my *transition* of being famous, I tried to ask God why was I here? what was my purpose? Surely, it wasn’t just to win three gold medals. There has to be more to this life than that.”

—Wilma Rudolph (1940–1994)