2

$D$ verifies $\langle M \rangle$ is a (deterministic) TM and then builds the configurations graph and checks if the initial configuration of $\epsilon$ is connected to an accept state (there are only finitely many) and returns true if there is and false if there isn't. The problem here is that, even if you define the TM so that there are only finitely many ...


2

I think you are really asking a question about the definition of the notion of well-foundedness. I think the notion of loop variants is a bit of a red herring here: I would argue that any reasonable definition of well-foundedness should enable proving that a loop is terminating iff there is a well-founded relation which acts as a variant for it, almost as a ...


2

Yes. See the notion of an approximation-preserving reduction.


2

The answer is $\bf 0''$ (and so in particular computation in the limit - which corresponds to $\le_T\bf 0'$ - is not enough). And this stronger result is also folklore (I was assigned it as an exercise way back when). As an upper bound we just check quantifier complexity: $\Phi_e$ runs in polynomial time iff there exists some polynomial $p$ such that for ...


2

There is no generally accepted definition of Turing machine. Various authors use various models. One author's definition might specify the output tape, another's might leave the choice to the Turing machine designer. The reason that we don't care about this "calling convention" is that it doesn't matter from the point of view of computability (and, to a ...


2

Your question is very philosophical in nature because you are asking about what is considered by computation and it’s physical implementations. In short, there is a ongoing discussion on different accounts of concrete computation e.g. the simple mapping account, the semantic account, the syntactic account, the mechanistic account, the causal, the ...


1

any location except i/p part means (total unbounded tape area - tape area that includes i/p string) = (infinity length - finite length) as we know i/p string length is always finite = infinity length in the definition of linear bounded automata it is stated that the tape can be used as a function of the input string length.but here the portion that can ...


1

Humans can solve some instances of undecidable problems and so can computers. Computers cannot solve all instances of undecidable problems, and not can humans.


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