-1
votes
0answers
20 views

Non trivial index set r.e problem [on hold]

suppose A is a non-trivial index set (type ) of natural number. am i right that the following sentence be false? A can be a set of index off all primitive recursive function?
-1
votes
0answers
47 views

Prove Computation Function Problem [on hold]

i read in one text book that: there is a computable function f such that for every y we have: how we can prove this sentence? in fact the TextBook is MARTIN DAVIS Computability ...
0
votes
1answer
35 views

Logic & Computability Problem

i read this sentence in one exam that be false. anyone could say why? if predicate H(x) become false when a program with code r(x) halt on input l(x), then H be a computable predicate.
-1
votes
1answer
47 views

Turing & Computability & Computation

We know if we have: we can show (T=t= Turin Redu.) but i have no idea why this relation be correct? any idea?
0
votes
0answers
50 views

Computation Challenging Problem [closed]

in one Book i see the following exercise: and we know following equation are hold? but i have no idea how the following be hold?
0
votes
0answers
49 views

TAUTOLOGIES NP-Complete Condition

The decision problem TAUTOLOGIES is, Given $\forall x_1 \forall x_2 ... \forall x_n$ $\phi(x_1, x_2, ... x_n)$ a set of universally quantified Boolean variables and a Boolean formula ...
0
votes
0answers
66 views

Primitive Recursive Predicate Challenge

I'm an Computer scientist, and I recently ran into a challenge. If we have primitive recursive predicate $P(x), Q(x)$, I think that all of following 4 expressions can be primitive recursive. Any hint ...
0
votes
0answers
36 views

Recursive Set and Complement Problem

if we have $$A=\{x:|W_x\ne\phi\}$$ can we say always my tight listed below is true? $A$ is recursive , $A$ is r.e, complement of $A$ is r.e, complement of $A$ is not recursive?
0
votes
1answer
57 views

Recursive Set Challenge

we knoe also we know for example if A be any arbitrary r.e set. can we always Necessarily the following is TRUE ? (always) any description is good. (bar sign means complement)
0
votes
1answer
43 views

Complexity & Computation & Logic Problem [closed]

As i study for prepare to CS Final exam, i have some challenges. can i say all of following statements are true? 1) each infinite recursive set, is union of two disjoint infinite recursive set? 2) ...
1
vote
3answers
68 views

How does one generally use partial function in logical statements?

How does one generally use partial function in logical statements? How it's done in practice? Specifically, let $M$ by a Turing machine, $f_M:\{0,1\}^*\to\{0,1\}$ the characteristic function which ...
2
votes
1answer
36 views

Undecidability of REGULAR_TM

In case you have Sipser's Introduction to the Theory of Computation 3rd edition, I am asking specifically about the proof of theorem 5.3, how the language REGULAR_TM is undecidable. \begin{equation} ...
4
votes
2answers
291 views

Why is propositional logic not Turing complete?

According to 1 (probably not the most relevant source), propositional logic is not Turing complete. Aren't all computations in computers performed using logic gates, which can be represented as ...
4
votes
1answer
103 views

How many digits of Chaitin's $\Omega$ constant would we know if we had a $\Sigma_1$-Oracle?

According to Wikipedia (and it seems intuitive from the definition itself), $\Omega$ is Turing equivalent to the halting problem and thus at level $\Delta_2^0$ of the arithmetical hierarchy. Do this ...
6
votes
4answers
451 views

Is the set of PA theorems the same as the set of solvable halting problems?

I am not sure if this is a trivial question. By Post's theorem we know that every PA (first order logic) theorem is equivalent to stating that a given input C in a given Turing machine halts or ...
3
votes
1answer
118 views

Question about $\Sigma_n$-soundness

According to wikipedia (http://en.wikipedia.org/wiki/%CE%A9-consistent_theory#Definition): "$\Sigma_n$-soundness has the following computational interpretation: if the theory proves that a program C ...
1
vote
2answers
171 views

I do not understand why the Turing computable sets of N are exactly the sets at level $\Delta_1^0$ of the arithmetical hierarchy

The reason I don't understand it is this. Take for example the twin primes conjecture, which is $\Pi_2^0$. The set of twin primes is computable right? (there is a Turing machine that enumerates all of ...
1
vote
1answer
73 views

Seeking Alternate Proof Regarding Closure Of Recursively Enumerable Languages Under Shrink

So I would like to show that the class of Recursively Enumerable languages are closed under the shrink operation. In other words, $\mathrm{shrink}_a(L) = \{x \mid x=\mathrm{shrink}_a(w), w\in L\}$ and ...