**3.108 complexity-theory questions.**

I have read that checking if tuple belongs to join of two tables is NP-complete.
I had computional-complexity activities during my studies, I remember basics, however I have forgotten details. ...

I know for an LBA the emptiness problem is undecidable. However I am not clear on how to reduce the halting problem of Turing machines to this as LBAs are strictly computationally less powerful than ...

In reading some blogs about computational complexity (for example here)I assimilated the notion that deciding if two groups are isomorphic is easier than testing two graphs for isomorphism. For ...

The Wikipedia page on zero-knowledge proof says
Zero-knowledge proofs are not proofs in the mathematical sense of the term because there is some small probability, the soundness error, that a ...

Let
$$ L_{300}=\{\langle M,w\rangle \mid M\text{ prints more than }300\text{ non-blanks on input }w\}.$$
Is $L_{300}$ decidable?
My intuition is it is decidable because given $M$ and $w$, we need ...

It is NP-hard to approximate maximum 3D matching problem even if each element occurs exactly in two triples. I'm interested in the following decision version of 3D matching.
Informally, Given a set ...

I was reading the following paper by Jim Kadin, "$P^{NP[O(\text{log } n)]}$ and sparse Turing complete sets for NP"
The main result is that if there is a sparse set $S \in NP$ such that $coNP \...

The fact that PPAD is a subclass of TFNP seems to be taken as evidence that PPAD cannot be shown complete (or hard) for classes of independent interest like NP ∩ coNP. Slightly confusing, it even ...

The problem: Exact Cover by 3-Sets (X3C)
The definition: Given a set X, with |X| = 3q (so, the size of X is a multiple of 3), and a collection C of 3-element subsets of X. Can we find a subset C’ of ...

A common approach to decide whether two given graphs are isomorphic is to compute the so-called canonical label (alternatively, canonical graph) of each graph and to check whether those match or not.
...

From $P\subseteq \oplus P \subseteq PSPACE$ and $P\subseteq PP \subseteq PSPACE$ we infer $\oplus P\neq PP$ gives that
$$P\neq PSPACE.$$
Are there any other consequences?

I have the following language : $L=\{\langle C_1,C_2\rangle \text{ | } C_1 \text{ and } C_2 \text{ are two circuits that calculate different function}\}$. We can call this language SAT-2C.
Prove that ...

The first problem is X3C for which I try to find out whether it's a special case of the second problem.
The second one is a stacking problem for which we have an itemset $I := \{i_1, ..., i_n\}$, $m$ ...

Question 1: Is it known that $\mathrm{QP}=\cup_{k}\mathrm{TIME}(2^{\mathrm{log}^k(n)})$ has any complete problem?
Question 2: Can this be used to simplify the computational complexity theory at all?

The time hierarchy theorem states that
$DTIME(f(n)) \neq DTIME(f(n)\log(f(n)))$
(Let me acknowledge that this statement isn't 100 percent accurate because f must be "time constructible" and ...

Adleman's theorem gives $$\mathsf{BPP\subseteq P/Poly}.$$
Why is this theorem considered progenitor to derandomization conjecture that $\mathsf{P=BPP}$?
Does it mean Adleman's result could be ...

I came across the following statement:
"Since b is smaller than n, the complexity $O((n + mb)^3)$ is polynomial."
I suppose it has something to do with the notion of polynomiality in terms of the ...

(At the very bottom of this, I will shortly describe the motivation for this question.)
Assume we have a commutative monoid $(G,\circ)$, i.e. a set $G$ with a commutative binary operation $\circ$ ...

It is common to define $P$-completeness with respect to logspace many-one reductions. I am looking for a complexity class $C$ such that if $C=P$ then all problems in $P$ are $P$-complete under many-...

The reduction from SAT to Clique shows a way to construct a graph with cliques from a Boolean formula. A closer look at that reduction even yields a simple algorithm which finds a large clique in the ...

So, I have two problems:
Minesweeper: given an undirected graph where some vertices have a whole number associated with them, check if there is a way to mark some of the non-numbered vertices such ...

I heard my teacher say that many theorists tend to be inclined to P!=NP. Why it is that and what is your personal intuition about this topic?
Thanks

In these notes about quantum computation by Scott Aronson, he explains that the computation classes $\mathsf{BPP}$ is contained in $\mathsf{BQP}$, but that they are not equal, and
So, the bottom ...

Recently, I've read Hennie's Paper. I understood the construction of buffer zones, but why can't it be applied to yield a single-taped Turing machine?

UPDATE: In 2 days, if no more convincing answer is posted, then bounty of 50 rep. will go to xskxzr. Due to lack of connectedness and a clean & clear cut, the bounty is still open for 2 days. (UTC ...

Follow-up question in the series:
Karp hardness of searching for a matching erosion
Karp hardness of searching for a matching split
Maximum Matching Cut problem
Input: An undirected graph $G(...

In Computational Complexity -- A Modern Approach, by Arora and Barak, they have the following claim (Example 3.6).
Let EXPCOM be the following language
$$ \{ \langle M, x, 1^n\rangle \mid M \text{...

First, read the previous question: Karp hardness of searching for a matching cut
As mentioned in the supposed-to-be-comment answer in that question, without the requirement of cardinality $k$, the ...

Our problem is: Given an undirected graph, does it have a vertex cover consisting of $k$ vertices?
A vertex included in this vertex cover variant will cover every edge incident to it and every edge ...

This is in a series of posts. Previous quetion:
Vertex cover with covering radius 2
Other series: Karp hardness of searching for a matching split
In this problem, our cover for a given undirected ...

How many messages are sent in the distributed system if the StateXevent-->action is like this
initiator × SP → {send(I,N(x)) to N(x); become done}
idle × Receiving(I,Z) → {Process(I); become ...

Background
I have a list of 50 million $A-A_i$ pairs, where $i>1$, and $A$ and $A_i$ are some text. I need to extract the $A$ values from the list, so I get a new list of unique $A$ values.:
$$
\...

I think that these two classes should be the same, but I can't find any literature about this and have a limited background on the topic.
This is my reasoning, and I would like to know if (1) this is ...

Input:I am provided with x and y.
x is a 32 bit non negative integer and y is some node-id of the tree.
So, I built a trie with 32-bit non negative integer values which are the keys associated with ...

this is related to the following question:
Generalised 3SUM (k-SUM) problem?
Without loss of generality, let's only consider even $k$, or just $k=4$.
My question is, after summing all pairs of ...

In computational machine learning, the notion of Probably Approximately Correct means that (generally speaking) we can find (or "learn") with a high probability a function which has "low error".
Is ...

Given: A Fully Quantified Boolean Formula (FQBF) where the quantifiers of the Boolean Variables alternate between $\exists$ and $\forall$ from left to right in the problem.
Query: Is the above ...

Given $L_1, L_2 \in NP$, $L_1 \cup L_2 \in P$ and $L_1 \cap L_2 \in P$,
Prove: $\ L_1, L_2 \in coNP$
What I've done so far is:
$$ L1 \cup L2 \in P \Rightarrow (L1 \cup L2) ^\complement \in P
\...

Is it good to define a language $\mathcal{L}$ in NP as a language for which, given an element $x$, it is possible in polynomial-time to check whether $x \in \mathcal{L}$ or not?
Because I need to have ...

Because my question is not clear and vague as indicated by Dr.I will rewritte it
First we know that the Problem of STCON is a complete problem in NL
So we have to make a DTM to solve it in a ...

Let $T=(V,E)$ be tree and each edge has a positive scalar weight. I need to print all paths in the tree and then sort the weight of edges in each paths. it needs $O(n^3\log(n))$ time. To solve this ...

What is the biggest complexity class that is low for each other equivalent definition of $\mathrm{PP}$?
I already know that $\mathrm{PP}^\mathrm{BQP}=\mathrm{PP}$. This is a lowness result using ...

We know $P\subseteq PH\subseteq PSPACE\subseteq EXP\subseteq NEXP$.
Is it known or believed that $\Delta_2^{exp}=EXP^{NP}\subseteq NEXP=\Sigma_1^{exp}$ and/or $EXP^{PH}\subseteq NEXP$?
Does $NP=coNP\...

All I could find is an example of sparse language.
I understand that I need to design a language whose all strings generation should not be bounded by a polynomial function, but I feel all the ...

Please, establish the above claim formally. It seems that the structure of complexity classes has so much bizarre features everywhere.
For the $\Longrightarrow$ direction, a padding technique will ...

Concerning about a wide variety of complexity classes, I have come up with the above conjecture.
Please, establish the claim in the title formally.

A subset $S$ of vertices in an undirected graph $G$ is called almost independent if at most 100 edges in $G$ have both endpoints in $S$. Prove that finding the size of the largest almost-independent ...

Given a graph $G=(V,E)$, metric spaces $\delta:E\rightarrow \mathbb{Z}^{+}$ and $w:E\rightarrow \mathbb{Z}^{+}$, terminal vertices $s,t\in V$, do there exists $s\rightarrow t$ path $P=(V_{p},E_{p})$ ...

- np-complete
- time-complexity
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- np-hard
- np
- space-complexity
- turing-machines
- satisfiability
- graph-theory
- polynomial-time
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- computability
- decision-problem
- p-vs-np
- reference-request
- terminology
- optimization
- circuits
- approximation
- algorithm-analysis
- oracle-machines
- asymptotics
- nondeterminism

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