# Re: more evil firmwares found

Jochen Voss <voss@seehuhn.de> wrote:
>
> On Fri, Apr 23, 2004 at 08:26:35PM +1000, Herbert Xu wrote:
>> Given any finite string of bits, you can construct a Turing machine in a
>> deterministic way and execute it.
>
> Sorry, I can't follow here. What do you mean by "construct a
> Turing machine in a deterministic way"? What would be the Turing
> machine for
>
> 101011110100000000000000110101000000000000111010100000001
Given any Turing machine M there is a Turing machine N that turns its
input s and writes out a new Turing machine M' that is equivalent to
M operating with s as the input.
This gives you a mapping (realised using N) from the set of finite strings
to the set of Turing machines.
Think of it another way, there exists a C program that can enumerate all
valid C programs. Just generate all strings of length 1, 2, etc. and use
gcc to validate its syntax (let's assume that gcc halts on all input :) and
print out the valid ones.
--
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Email: Herbert Xu ~{PmV>HI~} <herbert@gondor.apana.org.au>
Home Page: http://gondor.apana.org.au/~herbert/
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