Questions tagged [computability]
83 questions
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Why do we define equivalent turing machines as two turing machines with the same accepted languages?
From many textbooks about computability, I see how we define equivalent turing machines as follows:
Two turing machines TM1 and TM2 are equivalent <=> L(TM1) = (TM2)
where L(TM1) is the languages accpeted by TM1, i.e. L(TM1) = {w | TM1(w) = accept},…
Neil Zhang
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Equality between two propositions nat -> nat
I am currently working in a project in coq where I need to work with lists of nat -> nat. So basically I will have a definition that takes a list (nat -> nat) and a proposition f : nat -> nat as parameters and the goal is to retrieve the index of f…
Musher Soccoli
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Inputs to Program to Illustrate Halting Problem
Is this illustration of the haling problem correct?
function halts(func) {
// Insert code here that returns "true" if "func" halts and "false" otherwise.
}
function deceiver() {
if(halts(deceiver))
while(true) { }
}
If so, why do so many…
Robin Andrews
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"Reduction" from the complement of the universal language (L_u) to the language of nonempty-language Turing machines (L_ne)
I have a question from the domain of theoretical computer science.
The so-called universal language, L_u, is composed of pairs (M, w) such that w \in L(M). The language L_ne consists of machines M (actually, their descriptions, but let's not be too…
Luka Fürst
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How to define a function with Church numerals in lambda-terms?
How can I express the following function by a lambda term?
f(n) = T if n != 0.
F if n = 0.
n stands for a Church numeral.
I know that 0 := λf.λx.x where λx.x is the identity function and all other natural numbers can be expressed by n := λf.λx.f (f…
user3351676
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How to define a coding function for all finite subsets of N?
For working with countable sets I have to define a coding function of all finite subsets of N (natural numbers). How can I do this?
I started with finding a function for all natural numbers: f(n)=1+2+...+(n-1)+n. But how can I express a coding…
user3351676
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Proving the inexpressibility of a function in a given language
I'm currently reading through John C. Mitchell's Foundations for Programming Languages. Exercise 2.2.3, in essence, asks the reader to show that the (natural-number) exponentiation function cannot be implicitly defined via an expression in a small…
Ben
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Multiple questions related to Actor-based model
I have been told to write a paper that works as a review for Hewitt Actor-based model where I have to include:
a) Hewwit actor-model definition (done, with explanations about how "actors" work; disallow shared memory, etc).
b) Calculus example => I…
Francisco Javier
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Automata and Computability
How long will it take for a program to print a truth table for n propositional symbols?
(Symbols: P1, P2, ..., Pn)
Can't seem to crack this question, not quite sure how to calculate this instance.
jimmyb
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Determining a program's execution time by its length in bits?
This is a question popped into my mind while reading the halting problem, collatz conjecture and Kolmogorov complexity. I have tried to search for something similar but I was unable to find a particular topic maybe because it is not of great value…
user12546101
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vote
1 answer
Can a grammar ever be parsed by LL(1) but not with LR(1)?
For homework, I was given the following grammar:
S: D
D: AbBb | BaAb
A: ε
B: ε
I computed it using LL(1) just fine. The first sets were:
S: a, b
D: a,b
A: ε
B: ε
The follow sets were:
S: $
D: $
A: b
B: a,b
When I made my parsing table, the…
Ryan Foster
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Something is not computable, can it be co-recursively enumerable?
My understanding is since it is not computable, it may not halt when the answer is 'yes' or 'no'. That's why it cannot be co-recursively enumerable since it can't guarantee it always halts on 'no'.
sharprabbitz
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Does my solution show that the language is uncomputable by applying rice's theorem?
If p is a Turing machine then L(p) = {x | p(x) = yes}.
Let A = {p | p is a Turing machine and L(p) is a finite set}.
Is A computable? Justify your answer.
So I'm trying to figure out how to solve this question and here is the answer that I've come…
ken6208
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Show that the language L = {w ∈ {0, 1} ∗ | Mw(x) ↓ for an input x} is partially decidable but not decidable
I am trying to prove that the language L = {w ∈ {0, 1} ∗ | Mw(x) ↓ for an input x} is partially decidable but not decidable. Mw is an encoding of M, thus the language L is such that all encodings of machine M halt on some input x.
I have two…
Ponsietta
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Subset sum where the size of the subset is `k` is NPC?
I have a variation of Subset-Sum problem where the size of the subset is k and all the integers are positive (not zero).
As can be seen online, this question can be fairly solved using dynamic programming in pseudo-polynomial time.
I need to decide…
Mugen
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