computation-theory,turing-machines,np-complete,np,decidable , NP and 3-SAT and One Facts

## Question:

Tag: computation-theory,turing-machines,np-complete,np,decidable

any expert could help me why this sentence is True?

if L ∈ NP and L ≤p 3−SAT (i.e: reduce L to 3-SAT in poly time) then L is NP-Complete.

This statement is false. Since 3SAT is NP-complete, every problem in NP polynomial-time reduces to 3SAT, so if you choose any language in NP, then it will polynomial-time reduce to 3SAT. In particular, if you choose the empty language ∅, which is known not to be NP-complete, then ∅ ∈ NP and ∅ reduces toe 3SAT, but ∅ isn't NP-complete.

Hope this helps!

# Related:

## Running time of a program on deterministic and non-deterministic Turing machine

complexity-theory,time-complexity,turing-machines
I've found the following statement: If a program P for Non Deterministic Turing Machine solves a decision problem in time limited by a polynomial p(S), where S-size of input, then it can be run on a Deterministic Turing Machine, and the solution will be found in time limited in time...

## Turing Machine Binary Counter

java,binary,turing-machines
I decided for practice that I would create a binary counter simulating the methodology of a Turing Machine. To be specific, I plan to emulate the first example from this: (https://www.cl.cam.ac.uk/projects/raspberrypi/tutorials/turing-machine/four.html) Then I will go farther to create more for my machine! My adaption to this example is that I...

## Is finding a subset with exact cut with other given subsets NP-hard?

algorithm,complexity-theory,combinatorics,computation-theory
I am trying to figure out whether the following problem is NP-hard: Given G_1,..,G_n subsets of {1..m} c_1,..,c_n non-negative integers in {0..m} Find T subset of {1..m} S.T. for all i=1..n, T intersects G_i in exactly c_i elements I tried to find reductions to NP problems such as coloring, or...

## Specifying members of a given sequence with a Turing Machine

algorithm,math,turing-machines
One question I came across was, given a binary sequence a_0, ..., a_{n-1} how many transitions does it take such that when given a non-negative integer i it outputs a_i if i < n and 0 otherwise. You can assume the input starts with a 1 unless i is 0....

## NP and 3-SAT and One Facts

computation-theory,turing-machines,np-complete,np,decidable
any expert could help me why this sentence is True? if L ∈ NP and L ≤p 3−SAT (i.e: reduce L to 3-SAT in poly time) then L is NP-Complete. ...

## Sorting algorithm times using sorting methods

python,algorithm,sorting,time-complexity,computation-theory
So I just learned about sorting algorithm s bubble, merge, insertion, sort etc. they all seem to be very similar in their methods of sorting with what seems to me minimal changes in their approach. So why do they produce such different sorting times ie O(n^2) vs O(nlogn) as an...

## Fastest Way to Generate x Number of Random Variables

matlab,vectorization,computation-theory
index = [10 100 1000 10000 100000] Let's say I wanted to generate 10, 100,...,100000 (corresponding to index above) exponential random variables with parameter 1/10. I of course did this with a for loop and with the command for example x = exprnd(0.1,100,1) One can also generate the exponential random...

## Some inference about NP [closed]

algorithm,turing-machines,np,np-hard,turing-complete
this is my first question on this site. I‌ recently, study on NP. I have some confusion about this Topic, and want to propose my inference and some one verify me. I) each NP problem can be solved in Exponential Time. II) if P=NP then NP=NP-Complete. III) Problem of factorization...

## expressions in lambda calculus

lambda,functional-programming,computation-theory
am trying HARD AND FAILING to find how to express a question in Lambda.. Perhaps am mistaken in the search? As far as I understand, in Lambda calculus, we get to define the parameters, operations, etc. eg: TRUE := λx.λy.x FALSE := λx.λy.y AND := λp.λq.p q p OR :=...

## Why do we need to use the negation part in Turing's Halting Proof?

loops,logic,proof,turing-machines,halting-problem
For instance, let's say I have this Turing machine, H, which tells us whether or not a program and input will halt. Let's say we call H on itself. It has to give an answer, so if it prints out "does not halt" then didn't it technically halt to print...

## Turing Machine Arrow Definition

turing-machines
Does anyone know the exact definition of '=>', '<=' and '<=>' in the context of Turing Machines? Googling failed to provide me with the answer! To put it into context, here's a theorem / proof. _ Theorem A language L is decidable <=> both L and L' are Turing-recognisable. Proof:...

I'm trying to write a simple binary adding program in Python (I know Python can do it already, I'm just doing it to practice basic computing concepts). I got it to work pretty well, the only thing that is weird is that when one of the numbers is longer than...

## Can I use stack in Turing Machine?

finite-automata,automata,turing-machines,automata-theory
I am trying to design a Turing Machine that accepts the language L = {w | anb2n} where ∑ = {a, b}. For example machine accepts the input : "aabbbb" but does not accept the "aabb" My code is below about that language ; #include <iostream> #include <string> using namespace...

## How to match a set against a set of sets, completely

mapping,combinatorics,computation-theory,np-complete,set-theory
This problem is similar to the "Exact Hitting Set" problem (http://en.wikipedia.org/wiki/Exact_cover#Exact_hitting_set) but with slightly different constraints. I am looking for libraries, implementations, or papers that solve the following. Say I have a set of sets S, and is initialized as follows: S = {N, O, P, E}; N = {1,...

## What are the six basic primitives in Turing Complete

turing-machines,turing-complete
I am listening the edX lesson, and the professor stresses that every machine able to perform those six basic primitives can be called Turing Complete. But what are the six basic primitives?

## Language class compilable to heapless runtime

compiler-construction,programming-languages,computation-theory,memory-model,turing-complete
So in the general case, a program uses both memory in the stack (automatically managed) and heap (garbage collected or manually managed). What is the class of programs that can be compiled to use memory in a stack-like fashion only and no heap allocation? Is it still Turing-complete with some...

## Guidance on Algorithmic Thinking (4 fours equation)

algorithm,computation-theory
I recently saw a logic/math problem called 4 Fours where you need to use 4 fours and a range of operators to create equations that equal to all the integers 0 to N. How would you go about writing an elegant algorithm to come up with say the first 100......