English Dictionary

transition function

名詞

(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.

日本語の意味

状態と入力シンボルの組み合わせから、次に移る状態を決定する関数（状態遷移関数） / 計算理論において、与えられた状態と入力シンボルに基づいて、次の状態を示す関数

The transition function of the automaton maps each pair of current state and input symbol to the next state, determining how the machine moves when it reads a symbol.

オートマトンの遷移関数は、現在の状態と入力記号の組み合わせを次の状態に写像し、読み取った記号に応じて機械がどの状態に遷移するかを決定します。

意味（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.

意味（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,𝜑₁) and (U_2,𝜑₂) coordinate charts with U_1∩U_2≠∅, the transition functions 𝜑₁₂=𝜑₂∘𝜑₁⁻¹ and its inverse 𝜑₂₁=𝜑₁∘𝜑₂⁻¹ may be constructed.

If (U_1,𝜓₁) and (U_2,𝜓₂) are two complex charts, then the transition function is 𝜓₁₂:𝜓₁(U_1∩U_2)→𝜓₂(U_1∩U_2), given by 𝜓₁₂=𝜓₂∘𝜓₁⁻¹. We say M is a complex manifold if it has an atlas of complex charts (U,𝜓), such that all the transition functions are holomorphic, as maps from ℂᵐ to itself.

transition functions （ plural ）