transition function

English

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

Pronunciation

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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 $(U_1,{\phi }_1)$ and $(U_2,{\phi }_2)$ coordinate charts with $U_1\cap U_2\ne \mathrm{\emptyset }$, the transition functions ${\phi }_{12}={\phi }_2\circ {\phi }_1^{-1}$ and its inverse ${\phi }_{21}={\phi }_1\circ {\phi }_2^{-1}$ 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 ${\psi }_{12}:{\psi }_1(U_1\cap U_2)\to {\psi }_2(U_1\cap U_2)$, 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 ${ℂ}^m$ to itself.

Translations

function from (state, input symbol) to state

• Bulgarian: функция на прехода f (funkcija na prehoda)
• Finnish: siirtymäfunktio
• German: Übergangsfunktion f
• Romanian: funcție de tranziție f

homeomorphism between subsets of images of overlapping coordinate charts

• Bulgarian: функция на прехода f (funkcija na prehoda)
• Finnish: transitiokuvaus
• German: Übergangsfunktion f, Kartenübergang m, Kartenwechsel m

See also

• state machine
• coordinate chart
• atlas