Questions tagged [complexity]

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What’s the complexity of this decision problem with bit shifting?

I’ve been wondering about the computational complexity of a problem that involves bit shifting. Let me define some notation before I present the problem. If $\langle{b}\rangle$ is a bitstring ...
Sophie Weigle's user avatar
6 votes
3 answers
319 views

What are some examples of decidable Nautral Problems outside of EEXP?

I haven't really seen any examples of problems in complexity classes higher then EEXP. What are some examples of some primitive recursive problems outside of EEXP? Ideally with a large number of Es, ...
Colonizor48's user avatar
3 votes
1 answer
150 views

is SUBEXP contained within PSPACE?, NP?

Let SUBEXP is the complexity class of all problems solvable in sub-exponential time in the length of the input. What are the known properties of this class? Is it known to be contained in PSPACE, if ...
Colonizor48's user avatar
0 votes
0 answers
32 views

Hardness of finding minimal subsets that will change the maximum of a univariate polynomial

Given a univariate polynomial of the form $p(x) = \prod_{0 \leq i \leq N}{(x*a_i + b_i)}$ when all of the $a_i$ and $b_i$ are numbers in the range [-1,1] and $i$ goes from $0$ to $N$ (we are given all ...
Amit Bergman's user avatar
0 votes
0 answers
59 views

Prove that Vertex Cover is NP-Complete by reducing MaxCut to Vertex Cover

This is not the most straight forward reduction available on the internet since most people start from the fact that vertex cover is NP-complete and reduce a given vertex cover instance to MaxCut ...
Chaithanya's user avatar
7 votes
0 answers
79 views

How is FNP defined? Or, is FNP closed under relaxation?

I hope this isn't a dumb question, but I've been driving myself nuts regarding the following. The definition of $\mathsf{FNP}$ that I've found in many places is the following: A relation $R(x,y)$ is ...
Noah Stephens-Davidowitz's user avatar
0 votes
1 answer
67 views

What's the exact complexity of a DFS if we revisit nodes?

By "revisit nodes," I mean if we didn't maintain a set of nodes we have visited. So the sum I'm examining is just the number of paths from a root to a node, across all roots and nodes. We'll ...
Adam Jamil's user avatar
0 votes
1 answer
123 views

Complexity of "opposite" version of a variant of #Positive-2-SAT

In this post ,I introduced a new variant of #Positive-2-SAT . This version of problem puts restrictions on the inputs of the #Positive-2-SAT such that we can only choose at max only 2 clauses from ...
Anuj's user avatar
  • 13
4 votes
1 answer
222 views

Most Matrices are Rigid

The rigidity of a matrix $M\in \mathbb{F}^{n\times n}$ is the minimum number of entries that need to be changed in $M$ to reduce its rank to $r$. Formally, it is defined as: $$R_{M}^{\mathbb{F}}(r) = \...
atul ganju's user avatar
7 votes
1 answer
227 views

Is DFA language inclusion decidable in quasi-linear time? [duplicate]

Given two DFAs $A_1$ and $A_2$, we want to decide whether $\mathcal{L}(A_1) \subseteq \mathcal{L}(A_2)$. Of course, one can compute whether $\mathcal{L}(A_1) \cap \mathcal{L}(A_2) = \mathcal{L}(A_1)$. ...
Janmar's user avatar
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3 votes
0 answers
79 views

Extending fagin’s theorem for #P (for arbitary structure)

While i am reading Descriptive complexity of #P functions (Saluja) in theorem 1 he state that #FO coincides #P on ordered structures. This is a corollary from fagin’s theorem. I have read fagin’s ...
Omid Yaghoubi's user avatar
0 votes
0 answers
64 views

Is there some intuitive point to understand Co-NP/poly?

I know what it means: The coNP/poly problems are problems that decide a problem in co-nondeterministic poly-time using a $poly(n)$-size advice, where $n$ is the input size. By the definition, we have ...
Hanchun Yuan's user avatar
4 votes
0 answers
55 views

Reference for cost of translating between regular language formalisms

It is well-known that regular languages can be defined equivalently via many formalisms, among which regular expressions, NFAs, finite monoids, Monadic Second-Order logic (MSO). The cost (say in size ...
Denis's user avatar
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5 votes
0 answers
119 views

Are there well-accepted attempts of people to create complexity classes in continuous time?

I'm not in CS theory, but I've talked to a complexity theorist recently who, in passing, suggested that my research (not really analog computing, but hypercomputation using physical systems in ...
Daniel Primosch's user avatar
1 vote
0 answers
209 views

Cheapest Insertion is $2$-approximation for TSP

Consider the Cheapest Insertion Algorithm on a complete graph with $n$ vertices, where each edge $uv$ has a weight $w(uv)$, and the weights satisfy the triangle inequality $w(xz)\leq w(xy)+w(yz)$ for ...
Ioana Roman's user avatar
9 votes
1 answer
150 views

Validity problem of intuitionistic two-variable logic

The two-variable fragment $\mathrm{FO}^2$ consist of those sentences of first-order logic $\mathrm{FO}$ in which precisely two variables occur (e.g. $\exists x \exists y \exists z R(x,y,z)$ is not a ...
Reijo Jaakkola's user avatar
4 votes
0 answers
180 views

Any problems for which we know the complexity, but no algorithms with the same time?

I suddenly found myself wondering if there are any problems for which the complexity (time or space or anything else) is proven, say to be O(n^2), but for which the best known algorithms are worse ...
MinusPi's user avatar
  • 59
3 votes
1 answer
99 views

Recursive generic oracles

In Fenner, Stephen; Fortnow, Lance; Kurtz, Stuart A.; Li, Lide, An oracle builder’s toolkit, Inf. Comput. 182, No. 2, 95-136 (2003). ZBL1025.68041, the authors go through a variety of generic oracles. ...
veryinteresting's user avatar
1 vote
1 answer
167 views

Is QMA known to contain Co-NP?

Is QMA known to contain Co-NP? If not, would Co-NP being contained in QMA have any implications for other complexity classes. (e.g. Causing the polynomial heirachy to collapse.)
blademan9999's user avatar
6 votes
1 answer
259 views

What is the impact of encodings of sparse structures on the complexity of the model checking problem?

Some preliminaries first. Consider a purely-relational structure (a.k.a. database) $\mathfrak{A} = (A, R_1^{\mathfrak{A}}, \ldots, R_{|\tau|}^{\mathfrak{A}})$ over some finite signature $\tau = \{ R_1,...
Bartosz Bednarczyk's user avatar
2 votes
1 answer
86 views

Relative error estimation of a special type of GapP function

Consider the functions included in the complexity class GapP. We know that approximating a function from GapP, in the worst case, to inverse polynomial multiplicative error, is #P-hard. Even correctly ...
AngryLion's user avatar
  • 173
1 vote
0 answers
125 views

Deterministic one way communication complexity for message with arbitrary length

Let Alice have a binary string of length $n$ that it wants to send to Bob along a one-bit communication channel. However, Bob does not know the length of the message. I have been looking into ...
Koko Nanahji's user avatar
1 vote
0 answers
303 views

What is the computational complexity of the fastest algorithm to compute Jordan canonical form for a matrix

Given a matrix, What is the computational complexity of the fastest algorithm to compute Jordan canonical form for the matrix? suppose the value of elements of the matrix and eigenvalue are complex ...
XL _At_Here_There's user avatar
5 votes
1 answer
145 views

Different definitions of grammar complexity

It's known that there are different "kinds" of grammar complexity of language $L$ --- nonterminal complexity (minimal possible $|N|$ for grammar $(N, \Sigma, P, S)$ generating $L$), covering ...
DG_'s user avatar
  • 411
8 votes
1 answer
168 views

Generating a pseudo random Rubik's cube in $O(n^{2+\epsilon})$ time

Recently I've begun considering how one could generate and solve an $n \times n\times n$ Rubik's cube for $n$ well over 10,000. To solve such a cube is feasible; easily implementable parallelizable ...
Daniel Monroe's user avatar
3 votes
1 answer
153 views

CNF encoding of set cover - NExpTime-completness

Notation: given a CNF formula A over variables X, we write $[A(X)]$ for the set of valuations $v: X \to \{0,1\}$ such that $A(X/v)$ is true, i.e. the set of valuations that makes formula A true. I ...
Jean-Francois Raskin's user avatar
9 votes
0 answers
149 views

Is 4-Coloring restricted to graphs with crossing number 1 NP-complete?

Planar graphs are 4-colorable. Determining if a planar graph is 3-colorable is NP-Complete. A graph with a crossing number 1 (graph such that it can be drawn with $\le 1$ crossing) is 5-colorable. ...
William Gasarch's user avatar
1 vote
1 answer
97 views

Is there significance to the ratio of the time it takes to locate a problem's solution over the time it takes to verify the solution?

I believe I have found a problem, the solution to which can be verified in 0 time (the solution can only be located in non-zero time, however). As a result, the ratio of the time required to locate a ...
Francis J. Merrick's user avatar
6 votes
2 answers
395 views

On the complexity of a "list" datastructure in the RAM model

I am interested in the complexity of a data-structure equipped with the following operations (similar to a list): insertion of an element at a given position within the list deletion of an element at ...
Louis's user avatar
  • 775
11 votes
1 answer
503 views

The theoretical complexity of Go - The state of the art

What are the latest advances in theoretical complexity of Go? I know some early works about the complexity of Go: "Go is polynomial-space hard" proved that Go is PSPACE-hard. "Ladders are PSPACE-...
Blanco's user avatar
  • 421
0 votes
0 answers
251 views

Complexity of multi-objective optimization problems

How can we define and prove the worst-case complexity of multi-objective optimization problems (MOOP)? It is easy to see that, if one of the objectives is an NP-Hard optimization problem, then the ...
Iago Carvalho's user avatar
0 votes
2 answers
192 views

Fast algorithm to find pair of triangles with a common edge in a complete graph

Suppose we have a complete graph with 4 nodes. To each triangle in this graph we assign a value $energy$ that is the multiplication of its edge weights. The question is to first find pair of triangles ...
zhrmdi's user avatar
  • 13
8 votes
4 answers
686 views

Constraints on sliding windows

Let $L\subseteq \Sigma^*$ be a language of finite words and $n>0$ some integer. I would like to know if anything is known on the time and space complexity with respect to $n$ to check for ...
C.P.'s user avatar
  • 992
-1 votes
1 answer
233 views

Evidence integer multiplication is in linear time?

After millenia of quest we have identified two $n$ bit integers can be multiplied in $O(n\log n)$ time. Please refer details in https://www.quantamagazine.org/mathematicians-discover-the-perfect-way-...
Turbo's user avatar
  • 12.8k
14 votes
3 answers
3k views

What is a natural problem in theory of computation?

In Stephen Cook's paper on the P vs NP problem,[1] he states the following [2]: Feasibility Thesis: A natural problem has a feasible algorithm iff it has a polynomial-time algorithm. My question ...
Curious Yogurt's user avatar
16 votes
0 answers
275 views

Does small circuits for a NP-complete problem contradict ETH?

The remarks of the Theorem 4 in the paper "On the complexity of circuit satisfiability" claims that: if circuit satisfiability (CktSat) problem can be decided by deterministic circuits of $2^{o(n)}$ ...
Jacobs's user avatar
  • 161
10 votes
1 answer
1k views

Is convex optimisation in P?

Consider a convex optimisation problem in the form $$\begin{align} f_0(x_1, \ldots, x_n) &\to \min \\ f_i(x_1, \ldots, x_n) & \leq 0, \quad i = 1, \ldots, m \end{align}$$ where $f_0, f_1, \...
Sergey Dovgal's user avatar
1 vote
0 answers
74 views

Sentences in what kinds of grammar in the Chomsky hierarchy can be parsed by an LSTM of a given size?

Given an LSTM $N$ of a given size $A$, a sentence $S$ with a given number of words $B$, a Chomsky grammar hierarchy level $C$ in 0-3, a Chomsky grammar $G$ of level $C$ of size $D$, A given fixed, ...
Lars Ericson's user avatar
2 votes
0 answers
71 views

Looking for Research in Cryptographic Computing

I recall reading in college about a nascent research area regarding cryptographic techniques for secure computing, relating to zero-knowledge proofs, but I am having trouble remembering the exact term....
Kevin Dolan's user avatar
8 votes
0 answers
212 views

SAT Solvers and their applications

I've been reading and learning about SAT solvers this week. If they can solve problems with thousands of variable quickly haven't we practically solved ANY problem that can be reduced to it, including ...
Code_Newbie's user avatar
5 votes
1 answer
450 views

Is there a counterexample to this work?

Is there a counterexample to this claim https://arxiv.org/abs/1610.00353? They claim a $O(n^6)$ LP model with simulations to support. I think asking validity is not a reasonable problem. However ...
Turbo's user avatar
  • 12.8k
11 votes
0 answers
389 views

Error in paper "Some NP-complete geometric problems"?

The paper in question: M.R. Garey, R.L. Graham and D.S. Johnson. Some NP-complete geometric problems . This paper proofs the NP-completeness of some well-known problems, such as the Steiner Tree ...
J. Schmidt's user avatar
6 votes
1 answer
229 views

Paths of length $p$ in a Graph, $p$ a prime

I came across the following decision problem, for which I wondered whether anybody of you came across a similar problem and can give me some insight on its nature/complexity. Given as input a ...
gerald's user avatar
  • 61
3 votes
0 answers
777 views

Implications of resolving $BPP$ vs $PSPACE$

The relationship between the complexity classes $BPP$, $P$, and $NEXP$ is currently undetermined. We know that $P \neq EXP$ by the time hierarchy theorem, but we don't know if $BPP = P$ (as many ...
Mike Battaglia's user avatar
-1 votes
2 answers
1k views

Are these problems in NP class?

${\bf New\ version}$ [Version 1.2] Let $f: \mathbb{N} \to \{0,1\}$ be a computable function, ${\bf Fin}(\mathbb{Z})$ be the set of all finite subsets of $\mathbb{Z}$, and $W: {\bf Fin}(\mathbb{Z}) \...
TDThu's user avatar
  • 7
0 votes
1 answer
176 views

Does $\textbf{PCP}[poly(n), O(1)] = \textbf{coRP}$?

Something has been buzzing me recently. It is well-known that $\textbf{PCP}[poly(n), 0] = \textbf{coRP}$, but does $\textbf{PCP}[poly(n), O(1)] = \textbf{coRP}$ ? I have found a proof for this ...
Askannz's user avatar
  • 13
2 votes
1 answer
309 views

Petri net termination

Termination is the following problem. Input: a Petri Net with initial marking Output: "yes" iff there exists an infinite firing sequence. The naive algorithm in the case of bounded nets for example ...
Alberto's user avatar
  • 191
28 votes
2 answers
880 views

Formally Verified Complexity Theory

Is there any ongoing project to formally verify the theorems and proofs of complexity theory using a proof assistant like Coq? Are there any boundaries to doing this?
Samuel Schlesinger's user avatar
1 vote
1 answer
418 views

Complexity of the Schönhage–Strassen algorithm

In the Wikipedia article, the complexity is listed as $O(n \cdot \log (n) \cdot \log (\log (n)))$, where $n$ is the number of bits. Would the real bound be given by setting $n=\frac{b}{w}$, where $b$...
Arjun P's user avatar
  • 21
15 votes
1 answer
412 views

Parallel Pebble Game on a Line

In the pebble game on a line there are N+1 nodes labelled 0 through N. The game starts with a pebble on node 0. If there is a pebble on node i, you can add or remove a pebble from node i+1. The goal ...
Craig Gidney's user avatar
  • 1,498