4 votes
Accepted

Turing Machines time complexity with regard to the NP and P problem

What are the 'advantages' of a deterministic TM over the non-deterministic one? The advantage of the deterministic TM is that deterministic Turing Machines represent the type of computation we are ...
user avatar
  • 1,035
3 votes
Accepted

Worrying about details: high-level arguments about polynomial-time computability

The way you convince yourself of those claims is that you figure out how to write out an explicit proof of them. This same issue occurs with every mathematical proof. Every mathematical proof has ...
user avatar
  • 141k
3 votes
Accepted

Limited tapes-version TM for pair sum

Summary: There is no need to sort the given numbers since whether there are two numbers in $A$ such that their sum is $\alpha$ depends on the set of numbers in $A$. Since the choices for the set of ...
user avatar
  • 34k
3 votes
Accepted

Can a Turing machine quickly move to any position of a large string?

It depends. 1: If there are at least $\lceil \lg |s| \rceil$ unused cells after the end of $s$ and the head starts within $s$, then the answer is yes. Here is how. Start from the beginning of $s$. ...
user avatar
  • 141k
2 votes
Accepted

Turing Machine writes "a" for every input w is undecidable

Your suspicion is well-founded. The point 4 is invalid. Imagine the exact moment N "writes 'a' on the tape and reject" in the point 4. That means at that moment, it is known that M loops. ...
user avatar
  • 34k
1 vote
Accepted

Are deterministic Turing machines as powerful as probabilistic Turing machines?

This is a famous open problem in computer science theory. In particular, it comes down to whether BPP = P. It is widely conjectured and suspected that BPP = P, or in other words that randomness does ...
user avatar
  • 141k
1 vote
Accepted

Determining whether the problem of given a turing machine figuring out whether the language it accepts is the set of prime length inputs is R.E

I think your reduction is correct. Indeed, the reduction is clearly computable and furthermore if the original Turing machine $M$ halts on (the fixed) input $w$, then the set of words accepted by the ...
user avatar
1 vote

If A is Turing-reducible to B and B is Turing recognizable then A is Turing recognizable

The statement is false. Consider the language $H$ of the halting problem and let $H'$ be its complement. $H'$ is Turing reducible to $H$ and $H$ is recognizable, however $H'$ is not recognizable (if $...
user avatar
  • 23.3k
1 vote

Decidability of intersection of regular and decidable languages

I don't quite understand what you mean by if (A) is decidable then it is a language in R, if you mean that A is regular and B is regular then the intersection of two regular languages is still regular....
user avatar
1 vote

How is the computational power of a human brain comparing to a turing machine?

Here is a question on Turing completeness of neural networks. In my answer, I also discuss the human brain a bit, and I reference also this question here. I think allowing for some type of infinite ...
user avatar
  • 111
1 vote

Is there a TM that halts on all inputs but that property is not provable?

The halting of one TM can be encoded by constructing another TM and asking whether it halts. That is, given TM $T_1$ and input $I_0$, we can construct a TM $T_2$ with inputs indexed by the natural ...
user avatar

Only top scored, non community-wiki answers of a minimum length are eligible