What is the “description” of a Turing machine?

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I am currently reading about the Halting Problem in my course on the theory of computation and the following was given in my lecture slides



enter image description here



Now my question is that if $d$ is the description of a Turing machine, what exactly is $d$ from a strictly mathematical point of view? The way that $d$ is written above seems to suggest that $d in Q$ (i.e. that $d$ is a state of the Turing machine $T$), but I can't be entirely sure.






turing-machines halting-problem







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  • Think of it as a listing of a program: a complete description of the TM, one which you could use to build the TM.
    – Rick Decker
    35 mins ago














up vote
1
down vote

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I am currently reading about the Halting Problem in my course on the theory of computation and the following was given in my lecture slides



enter image description here



Now my question is that if $d$ is the description of a Turing machine, what exactly is $d$ from a strictly mathematical point of view? The way that $d$ is written above seems to suggest that $d in Q$ (i.e. that $d$ is a state of the Turing machine $T$), but I can't be entirely sure.






turing-machines halting-problem







share|cite|improve this question





















  • Think of it as a listing of a program: a complete description of the TM, one which you could use to build the TM.
    – Rick Decker
    35 mins ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I am currently reading about the Halting Problem in my course on the theory of computation and the following was given in my lecture slides



enter image description here



Now my question is that if $d$ is the description of a Turing machine, what exactly is $d$ from a strictly mathematical point of view? The way that $d$ is written above seems to suggest that $d in Q$ (i.e. that $d$ is a state of the Turing machine $T$), but I can't be entirely sure.






turing-machines halting-problem







share|cite|improve this question













I am currently reading about the Halting Problem in my course on the theory of computation and the following was given in my lecture slides



enter image description here



Now my question is that if $d$ is the description of a Turing machine, what exactly is $d$ from a strictly mathematical point of view? The way that $d$ is written above seems to suggest that $d in Q$ (i.e. that $d$ is a state of the Turing machine $T$), but I can't be entirely sure.






turing-machines halting-problem




turing-machines halting-problem






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  • Think of it as a listing of a program: a complete description of the TM, one which you could use to build the TM.
    – Rick Decker
    35 mins ago
















  • Think of it as a listing of a program: a complete description of the TM, one which you could use to build the TM.
    – Rick Decker
    35 mins ago















Think of it as a listing of a program: a complete description of the TM, one which you could use to build the TM.
– Rick Decker
35 mins ago




Think of it as a listing of a program: a complete description of the TM, one which you could use to build the TM.
– Rick Decker
35 mins ago










1 Answer
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The description is a string that encodes the formal specification of the machine, comprising:



  • the set of states,

  • the start state,

  • the set of halting states (or, where appropriate, the sets of accepting and rejecting states),

  • the tape alphabet,

  • the input alphabet,

  • the transition function.

Some authors also explicitly include the identity of the blank symbol in the description of the machine; others leave it to convention (e.g., stating that the alphabet will always be $c_1, dots, c_k$ for some $k$, and $c_1$ is the blank symbol).






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    The description is a string that encodes the formal specification of the machine, comprising:



    • the set of states,

    • the start state,

    • the set of halting states (or, where appropriate, the sets of accepting and rejecting states),

    • the tape alphabet,

    • the input alphabet,

    • the transition function.

    Some authors also explicitly include the identity of the blank symbol in the description of the machine; others leave it to convention (e.g., stating that the alphabet will always be $c_1, dots, c_k$ for some $k$, and $c_1$ is the blank symbol).






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      The description is a string that encodes the formal specification of the machine, comprising:



      • the set of states,

      • the start state,

      • the set of halting states (or, where appropriate, the sets of accepting and rejecting states),

      • the tape alphabet,

      • the input alphabet,

      • the transition function.

      Some authors also explicitly include the identity of the blank symbol in the description of the machine; others leave it to convention (e.g., stating that the alphabet will always be $c_1, dots, c_k$ for some $k$, and $c_1$ is the blank symbol).






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        The description is a string that encodes the formal specification of the machine, comprising:



        • the set of states,

        • the start state,

        • the set of halting states (or, where appropriate, the sets of accepting and rejecting states),

        • the tape alphabet,

        • the input alphabet,

        • the transition function.

        Some authors also explicitly include the identity of the blank symbol in the description of the machine; others leave it to convention (e.g., stating that the alphabet will always be $c_1, dots, c_k$ for some $k$, and $c_1$ is the blank symbol).






        share|cite|improve this answer












        The description is a string that encodes the formal specification of the machine, comprising:



        • the set of states,

        • the start state,

        • the set of halting states (or, where appropriate, the sets of accepting and rejecting states),

        • the tape alphabet,

        • the input alphabet,

        • the transition function.

        Some authors also explicitly include the identity of the blank symbol in the description of the machine; others leave it to convention (e.g., stating that the alphabet will always be $c_1, dots, c_k$ for some $k$, and $c_1$ is the blank symbol).







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        share|cite|improve this answer










        answered 3 hours ago









        David Richerby

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