491 views

### Can someone provide an introductory example of a certificate in complexity theory? [duplicate]

Just stepping into complexity theory, I am befuddled by this notion of a certificate and can't find any utility of this concept. From my understanding, a certificate is used when you are trying to ...
364 views

### Is it immediately true that the class of P is a subset of the class NP? [duplicate]

Forgive me if this is a stupid question - it's been a while since I thought at all about complexity theory and I want to make sure that I have covered all the possible angles with regards to the ...
203 views

### Can someone explain in a simple way what “reducible” mean in complexity theory? [duplicate]

I find the word "reducible" used in complexity theory not very intuitive, and too general taken on a face value. What does it exactly mean by problem A reducible to B? Does it mean that A can be ...
271 views

### How is the complexity of algorithms to solve 3CNF (decision problem) specified? [duplicate]

For k inputs, the complexity of naive algorithm is O(2^k). I understood this one. What is meant by "the size of the instance to be solved should be polynomial in k". Is it equivalent to the statement ...
150 views

### complexity theory NP [duplicate]

Ok, I really need help because I have read in so many books but still don't understand the complexity class NP. These are the books: Theoretische Informatik; Katrin Erk, Lutz Priese (german) ...
150 views

### How do we know that all NP problems reduce to NP-hard problems? [duplicate]

For example, how is it proven that any NP problem can reduce to subset sum, circuit satisfiability, etc.? Or could you link to a proof?
67 views

### P versus NP and what we are looking for [duplicate]

I was reading the other day about this problem, refreshing it, and on a couple of places over the internet I read somebody explaining something in the line of '..does not matter as long as is ...
101 views

### Does classification of a problem also require the algorithm used? [duplicate]

Just learnt that a problem in computer science can be divided into the following categories Polynomial problems NP problems NP hard problems NP complete problems ...
44 views

### Why does $L\subseteq \textbf{P} \cap \textbf{NP}$ is $\textbf{NP}$-complete imply $\textbf{NP} = \textbf{P}$? [duplicate]

If I show that a language $L$ is contained in $\textbf{P}$ and $\textbf{NP}$ and I know that the language is $\textbf{NP}$-complete, why did I proof that $\textbf{P} = \textbf{NP}$?
112 views

### The defining property of problems in NP [duplicate]

I'm coming to Computer Science from Mathematics and am familiar with the idea of building classes of objects using Propositional Logic. Namely, start with some universe of objects, define some ...
51 views

### Given an integer n, print all integers from 1 to 2^n. Why does this not prove that P!=NP? [duplicate]

I only just recently learned about the P=NP problem in introduction to algorithms class, and I'm still trying to wrap my head around it. I thought of this situation while cleaning my room today and ...
69 views

### Reducible and NP Hard [duplicate]

I have been confusing a bit about these relationship: Given A polynomial reducible to B 1/ If A is NP hard, what is the hardness of B? 2/ If B is NP hard, what is the hardness of A? 3/ If A has ...
55 views

### Why proving the solution of a problem is polynomial time is sufficient enough to say that it is a NP prolbem? [duplicate]

Why proving that we can verify the solution of a problem is polynomial time is sufficient enough to say that the problem is nondeterministic polynomial time? Please note: this is not a question on how ...
I am trying to understand the definition / meaning of reduction. Is it correct to say that the statement "Problem $A$ reduces to Problem $B$ in $x$-time" is the same as writing $A \leq_{x} B$? For ...