Question

please solve the problems(True/False questions)

25. There is a problem solvable by Turing machines with two tapes but unsolvable by Turing machines with a single tape 26. The language L = {(M, w) | M halts on input w} is recursively enumerable 27. The language L = {(M,w) | M halts on input w is recursive ne language L = {a"o"c" | n 2 1} in linear time 24. Nondeterministic Turing machines have the same expres siveness as the standard Turing machines.

Answer 1

Solution :

25 : There is a problem solvable by turing machines with two tapes but unsolvable by turing machines with a single tape : False
The turing machine with single tape and multiple tapes has same power. The single tape turing machine has infinite tape so it can be divided in two tapes and can be used to generate same language accepted by two tape turing machine. hence Any language generated by two tape turing machine is also generated by single tape turing machine.

26 : The language L = {<M,w> | M halts on input w} is a recursively enumerable : True.
The recursively enumerable language is a language that is recognizable. The turing machine for recursively enumerable languages halts for all input string w when w is accepted by language and it may or may not halt for input string w when we doesn't belong to the language. We can create a turing machine that halts on accepting strings and may or may not halt on non accepting strings for given language. Hence L is a recursively enumerable.

27 : The language L = {<M,w> | M halts on input w} is a recursive language : False
The turing machine generated for language may or may not halt on input string w when w is not accepted by M. Hence turing machine created for L may or may not halt. The recursive languages are decidable. So the turing machine must halt for all inputs in case of recursive language. hence the language L is not recursive as turing machine for L may or may not halt on some input.

24 : Non-deterministic turing machines have the same expressiveness as the standard turing machine : True
All turing machines has same expressiveness.

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