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I'm considering the turing machines with the following form: $(Q,\Gamma,b,\Sigma,\delta,q_0,F)$ where the tape symbols,$\Gamma$ are $\{0,1\}$, so the input symbols, $\Sigma$ must be $\{1\}$ and the blank symbol, $b$ is $0$. The set of states, $Q$, initial state $q_0$, final states $F$ and transition function $\delta$ can be arbitrary(in order to be a turing machine).

Is there a name for this type of turing machines?

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