Theoretical Foundation of CS….Define the following problems as predicates or membership problems for sets and prove whether or not they are solvable.
a) If an arbitrary Turing machine halts for all even numbers.
b) Whether an arbitrary Turing machine has over 176 instructions.
c) If you will get an A in the next computer course you take.
a) the given arbitary turing machine is not solvable.
actually it is not solvable by the turing machine provided by turing.
but you can create a turing machine that can generate even numbers i.e 2,4,6,8…., one after another and checks whether it satisfies the even number property or not.
the machine halts the first number having the property otherwise it continues to the next number.
these can be solved by using reimenn hypothesis.
b)it is also unsolvable.
this can be breifly known in busy bevear problem or by halting problem.
c)it is also unsolvable.
because as we doesnt know the behaviour of the machine and the halting problem is undecidable over a turing machine
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