You seem stuck with a logical problem.
From the fact that there are books that you cannot read, you cannot
infer that you cannot read any book.
Saying that the halting problem is undecidable for Turing Machines (TM)
only means that there are machines for which there is no way to determine
whether they halt or not by some uniform procedure that will always halt.
However there are Turing Machines that do halt. Now take a subset of
Turing Machines, called the Nice Turing Machines (NTM), such that it
contains only Turing Machines that do halt if and only if the tape
contains an even number of symbols. If a machine M is known to be from
that set, you have a simple way to decide whether M will halt: you
check whether the number of tape symbols is even (it requires only two
But that procedure will not work for TM that are not in the NTM set. (too bad!)
So the halting problem is decidable for the NTM, but not for the TM in
general, even though the NTM set is included in the TM set.
This is actually critical, and sometimes forgotten, when interpreting
It may well be that one can prove that an important property is
undecidable for a very large family of mathematical or computational
This does not mean that you should stop looking for a solution, but
only that you will not find one for the whole family.
What you may then do is identify relevant subfamilies for which
solving the problem remains important, and try to provide algorithms
to decide whether the property holds for members of that smaller
Typically, halting is undecidable for TM in general, but it is
decidable, often very simply, for large and useful families of
automata, which can all be seen as special cases of TM.