transition function

English

Two transition functions (2) illustrated by the arrows between the light blue areas below.

Noun

transition function (plural transition functions)

1. (computing theory) A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state.
2. (differential geometry) A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For $(U_{1},\varphi _{1})$ and $(U_{2},\varphi _{2})$ coordinate charts with $U_{1}\cap U_{2}\neq \emptyset$, the transition functions $\varphi _{12}=\varphi _{2}\circ \varphi _{1}^{-1}$ and its inverse $\varphi _{21}=\varphi _{1}\circ \varphi _{2}^{-1}$ may be constructed.

   Synonym: transition map

   • 2007, Dominic D. Joyce, Riemannian Holonomy Groups and Calibrated Geometry (Oxford graduate texts in mathematics)‎^[1], Oxford University Press, →ISBN, →LCCN, page 76:

     If $(U_{1},\psi _{1})$ and $(U_{2},\psi _{2})$ are two complex charts, then the transition function is $\psi _{12}:\psi _{1}(U_{1}\cap U_{2})\rightarrow \psi _{2}(U_{1}\cap U_{2})$, given by $\psi _{12}=\psi _{2}\circ \psi _{1}^{-1}$. We say $M$ is a complex manifold if it has an atlas of complex charts $(U,\psi )$, such that all the transition functions are holomorphic, as maps from $\mathbb {C} ^{m}$ to itself.

Translations

function from (state, input symbol) to state

• Finnish: siirtymäfunktio
• German: Übergangsfunktion f
• Romanian: funcție de tranziție f

homeomorphism between subsets of images of overlapping coordinate charts

• Finnish: transitiokuvaus
• German: Übergangsfunktion f, Kartenübergang m, Kartenwechsel m

See also

• state machine
• coordinate chart
• atlas