# 關於圖靈機接受的語言定義的困惑，一個非常基本的問題

$$M$$成為圖靈機，然後將接受的語言$$T（M）$$$$M$$的定義為$$T（M）= \ {x \ in \ Sigma ^ * \ mid z_0 x\ vdash ^ * \ alpha z \ beta;\ alpha，\ beta \在\ Gamma ^ *;z \ in E \}$$

Even in a deterministic Turing machine, the transition function $$\delta$$ may be a partial function i.e. there can be pairs of states and tape symbols for which the transition function is not defined. If the Turing machine is in state $$z$$ and reads symbol $$\alpha$$ and $$\delta(z,\alpha)$$ is not defined then it halts. Usually the accepting states $$E$$ are implemented by creating states for which the transition function is undefined for all inputs i.e. the Turing machine will always halt once it enters a state $$z \in E$$, regardless of the symbol it reads from the tape. You may also have other halting states, but if the machine halts in a state $$z \notin E$$ then it has rejected the input string.