Transition function: Difference between revisions

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In [[mathematics]], a '''transition function''' hasmay severalrefer different meaningsto:

* a [[transition map]] between two charts of an atlas of a manifold or other topological space

* the function that defines the transitions of a [[transition system]] in computing, which may refer more specifically to a

** [[Turing machine]],

** [[finite-state machine]], or

** [[cellular automaton]]

* a [[stochastic kernel]] In statistics and probability theory, the conditional probability distribution function controlling the transitions of a stochastic process

== See also ==

* In [[topology]], a ''transition function'' is a homeomorphism from one coordinate [[chart (topology)|chart]] to another. Given two charts (''U''_''i'', φ_''i'') and (''U''_''j'', φ_''j'') a transition function normally takes the form

* [[Non-analytic smooth function#Smooth transition functions]]

::<math>\phi_i\phi_j^{-1} : (U_i \cap U_j) \times F \to (U_i \cap U_j) \times F</math>

:for some set ''F'' being covered by the topology. See [[Atlas (topology)]] for additional details.

{{mathdab}}

* In [[computing]], a ''transition function'' is the function that defines the state transitions of a [[Turing machine]] or a [[state machine]].

{{disambig}}

[[Category:Mathematical disambiguation]]

[[fr:Fonction de transition]]