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Numbering Turing Programs

  1. Jan 10, 2012 #1

    jgens

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    Gold Member

    1. The problem statement, all variables and given/known data

    Assign a code number n(P) to every Turing program P.

    2. Relevant equations

    N/A

    3. The attempt at a solution

    Let pi denote the ith prime number. Let Q = {q0,q1,...} be internal states, let {B,1} denote tape symbols and let {L,R} denote direction symbols. Assign a code number to each of these symbols as follows: n(B) = p1, n(1) = p2, n(L) = p3, n(R) = p4, n(qk) = pk+5.

    Now suppose L is a line of a Turing program P. Then L = (qi,s,qj,s',X) where s,s' in {B,1} and X in {L,R}. Assign a code number to L as follows: n(L) = p1n(qi)p2n(s)p3n(qj)p4n(s')p5n(X).

    Lastly suppose that P = {L1,...,Lk} is a Turing program. Assign a code number to P as follows: n(P) = pn(L1)n(L1)...pn(Lk)n(Lk).

    This assigns each syntactic object we consider to a unique natural number. Moreover, this assignment is effective.

    Does this work?
     
  2. jcsd
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