Turing Machine Instruction Table
instructions, turing-machines
Solution
The Turing machine can already implement another Turing machine, and change its rules, say, to take as input a modifiable program. In particular, the Turing machine can compute any computable function. It could in theory implement a lisp interpreter, which would have macros, "self-modifing" code, etc.
So, the answer is NO. Remember, no one, and I mean absolutely no one person anywhere, ever, has actually wanted a Turing machine, though no doubt zillions of simulators have been written. (I won't admit to it, but as an undergrad I may have done something like that...) It's just something that various important proofs are based on.
Problem
The definitions of Turing Machine say that it is prohibited for one to read/modify it's instruction table (program). Exactly, Turing Machine has no access to it's own program. What benefits can be achieved if one could weaken this restriction? If a machine could analise and/or modify it's program. Would that extend the class of turing-computable tasks?