# Questions tagged [co-np]

Question about the complexity class that is a complement of NP, i.e. decision problems where the "no" instances can be accepted by a nondeterministic Turing machine that runs in time polynomial in the length of the input.

36 questions
Filter by
Sorted by
Tagged with
18 views

### Need clarification regarding certificates of coNP problems

NOTE: this is not an attempt to prove $NP \neq coNP$ There is one thing I have never been able to completely digest about the certificates of problems in $coNP$ and I would very much appreciate a ...
73 views

### A question about NP and coNP

It is an open question if NP $\neq$ Co-NP but if the conjecture were proved, this would mean that P $\neq$ NP because P is closed under complement. Now a fact that fails to enter my head is the ...
47 views

### Complement of languages and coNP

By definition, any language (decision problem) $L$ is defined as a subset of $\{0,1\}^*$, where $\{0,1\}$ is the alphabet. $L^c$ is said to be the complement of the language, and it seems to be ...
43 views

### Intersection of decision problems?

Say we have two problems $\Pi_1\in NP$ and $\Pi_2\in coNP$. Where does $\Pi_1\cap\Pi_2$ live?
56 views

### Are there any “complete” languages in $coNP -NP$?

Suppose $coNP \neq NP$ language B would be called "complete" in $coNP-NP$ if: $B\in coNP - NP$ $A\in coNP-NP \implies A\leq_pB$ Are there any "complete" languages in $coNP - NP$?
43 views

### Decision variation of max sat

I am trying to prove that following decison variation of MaxSAT is both NP hard and co-NP hard. $(\phi ,k) \in L$ iff an assignment of $\phi$ satisfies k clauses and no assignment satisfies more than ...
38 views

### Reduction of complement from complexity class co-np and p

Let P $\neq$ NP. D is in the complexity class co-NP. B is in the complexity class P. Let $\bar{D}$ be the complement of D, then $\bar{D}$ $\leq _ {p}$ B. Is this statement true or false? My ...
48 views

586 views

### How do I prove that SAT in coNP implies NP=coNP?

Is it true that if SAT is in coNP then its also coNP-complete (because it is NP-complete)?
188 views

### Showing a problem is in coNP

We have the problem $C = \{<G,S>| \text{ S is a minimal cover of G }\}$ and we want to show that $C\in coNP$. I can easily show that there's a ND TM that decides $coC$ using a guess to check if ...
1k views

### co-NP but not NP problems

What are the problems that are in co-NP but not in NP? i.e, those problems where incorrect strings can be deterministically verified in polynomial time but the correct strings can't be.
520 views

609 views

### An obvious approach to explaining NP != coNP, how far has it been pushed?

A recent question made me think about an obvious approach for circumventing the "algorithm is allowed to do anything" problem, when proving lower bounds. Instead of starting with a simple looking NP-...
156 views

### An obvious approach to NP = coNP, is there a counterexample?

Let's try to solve "co3SAT" with an NTM in polynomial time. It seems we need, more or less, to guess a proof that the formula is unsatisfiable i.e. derive a contradiction. We've got a formula in ...
2k views

### Why is NP not trivially equal to Co-NP? (a.k.a. what does Co-NP mean exactly?) [duplicate]

I've been trying to wrap my head around Co-NP, and how it's different to NP, but I am having some trouble. Co-NP is defined by Wikipedia as this: "A decision problem $\mathcal{X}$ is a member of co-...
180 views

### Some questions about NP / coNP / CSP

I need help with the following mock exam questions. True or false? 1.) If a non-trivial $(\neq \emptyset, \Sigma^*)$ finite set is NP-complete, then $P = NP$. True. Every finite set is in $P$ and ...