Questions tagged [reference-request]
Reference-request is used when the author needs to know about work related to the question.
1,488
questions
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28 views
Is there a primal-dual algorithm for the Tree Augmentation Problem or the Cactus Augmentation Problem?
The TAP problem and the CacAP problem can be seen as covering problems for the minimum cuts of a graph.
It seems like these problems would fall under the framework of network design problems (...
5
votes
1answer
156 views
Lower bound for the OR problem
Let us have booleans $x_1, \cdots, x_n$. Any algorithm that determines $\bigvee_1^n x_i$ with probability at least $2/3$ requires $\Omega(n)$ time. It is not too difficult to prove this, but the proof ...
3
votes
1answer
92 views
Regular Expressions that converts into unambiguous automata
Brüggemann-Klein and Wood (1992) proved that a certain kind of regular expressions, that they call “Deterministic Regular expressions”, when converted into automata using the Glushkov's Construction, ...
1
vote
0answers
51 views
Canonical tester for dense graphs: from tester to removal lemma?
A theorem of Goldreich and Trevisan [1] on property testing in the dense graph model states the following (docusing on the one-sided part):
Suppose there exists a one-sided testing graph algorithm ...
7
votes
2answers
133 views
Algebraic characterisation of star-free safety languages
It is known that star-free languages are definable by aperiodic syntactic monoids.
But is there any algebraic characterisation of star-free safety $\omega$-languages?
Edit: A language $L$ is safety if ...
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0answers
69 views
Large CLIQUE approximation
I am interested in algorithms to identify large cliques in graphs where the largest clique is a large fraction (definitely greater than half, perhaps as great as 4/5) of the total number of vertices.
...
3
votes
0answers
59 views
Exact FPT Algorithm for Continuous Euclidean $k$-Means
The continuous Euclidean $k$-means problem is defined as follows:
Given a set $X$ of $n$ points in $d$ dimensional Euclidean space $\mathbb{R}^{d}$. Given a parameter $k>0$, find a partitioning $P$ ...
2
votes
2answers
107 views
Status of certain problems in knot theory
I found it somewhat difficult to understand the status of certain problems from knot theory. Is it correct to say that it's been neither proved nor disproved that any of the following problems are NP-...
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52 views
Kolmogorov complexity with limited calculation time - edited
EDIT: After receiving the comment of Emil Jeřábek, I posted a more advanced question on a related topic, please also have a look at it.
ORIGINAL QUESTION
The Kolmogorov complexity of a string is the ...
0
votes
1answer
93 views
Diophantine equations with bounds on variables
Solving Diophantine equations is famously known to be undecidable. What about Diophantine equations to be solved over a finite domain? In particular, if I put an upper bound $k$ over the value of the ...
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0answers
53 views
EXPSPACE-complete problems involving numbers
This is a subset of this question. I'm looking for EXPSPACE-complete problems, for using in a reduction, which involve numbers in some ways, since my target problem involves numbers and linear ...
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0answers
71 views
Low-Treewidth Sorting Networks
It was previously asked if there exist Boolean circuits of treewidth $O(\log n)$ that compute the majority function $\text{MAJ}_n$ on $n$ inputs. While a construction using online algorithms and the ...
2
votes
1answer
91 views
Property testable in sublinear time in bounded degree graphs but not in general graphs
Is there some natural property that is testable in strongly sublinear time (i.e. $O(n^{1-\epsilon})$ for some $\epsilon > 0$) in bounded-degree graphs but not in general graphs? If not such ...
1
vote
1answer
203 views
Is this a novel technique for determining whether or not two rotated rectangles collide?
I was trying to determine whether or not two rectangles rotated around their centers were colliding and randomly thought to try the following algorithm:
Rotate both rectangles by the negative rotation ...
1
vote
0answers
83 views
Input length and calculation time to simulate a quantum measurement
Let us consider $n$ quits $b_i$. Let us start from the state $|0,0,...,0>$ and apply a circuit $C$ composed by $m$ quantum gates, with $m$ polynomial in $n$. The final state is $C|0,0,...,0>$. ...
4
votes
1answer
108 views
What is tightest known (VC-style) sample complexity bound for uniform convergence of empirical means?
The following result is adapted from Anthony and Bartlett, 1999 (Theorem 4.9).
Theorem There exist positive constants $m_0 \le 400$, $c_1 \le 8$, $c_2 \le 41$, $c_3 \ge 1/576$ such that, if $(\Omega,\...
-3
votes
1answer
105 views
Can I research in web technologies with an academic approach?
I'm an undergraduate computer engineering student. I know that I like to become a researcher in my major in the future. I also work as a junior web developer at a small start-up, and I think I really ...
4
votes
1answer
191 views
Does this notion of entropy have a name?
Recently I stumbled upon the following notion of entropy which seems quite natural to me. I am looking for its "real" name and/or any references where it might come up. I tried searching ...
1
vote
1answer
110 views
Communication complexity of reconstructing a random bit-string of length $n$
This seems like a folklore claim but I cannot find any reference to it. If Alice has a bit-string of length $n$ where each entry is independently set to 0 or 1 equiprobably, and Bob's goal is to ...
2
votes
0answers
65 views
Complexity of (Graph) Ramsey Theorem in Sum-of-Squares Proof System
(One formulation of) Ramsey's theorem states that any colouring of edges of the complete graph with $4^n$ vertices with two colours will contain a monochromatic clique of size $n$. I am new to proof ...
10
votes
1answer
223 views
Succinctness of regular expressions with empty word
Consider regular expressions on some alphabet $\Sigma$, without the empty word: $$e,f:=a\in\Sigma\mid e\cdot f \mid e+f\mid e^+$$
These $\varepsilon$⁻free expressions can define all regular languages ...
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44 views
Low Rank Approximation of a hidden subset
Let $P$ be a set of $n$ points in $\mathbb{R}^d$ and $Q\subseteq P$ with $\vert Q\vert \geq \alpha n$ for some constant $\alpha\in(0,1]$. Given a $j$-dimensional affine subspace(flat) $F$ consider the ...
1
vote
1answer
135 views
The "electricity packing" problem
In a distant village, there are $n$ electricity consumers. Consumer $i$ has a power demand of $d_i$ watts. The total electricity supply is $s$ watts. If $s\geq \sum_{i=1}^n d_i$, then all consumers ...
1
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0answers
38 views
A variant of k-median clustering
Suppose $\mathcal{P} =\{P_1,\cdots,P_n\}$ is a family of $n$ finite sets in $\mathbb{R}^d$. Given set $C=\{c_1,\cdots,c_k\}$ of $k$ points, consider the follwoing objective funtion
$cost(\mathcal{P},C)...
2
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0answers
67 views
Reference request: characterisation of simultaneous substitution
For simply typed λ-calculus, a simultaneous substitution from $\Gamma$ to $\Delta$ is concretely a type-preserving map from variables in $\Delta$ to terms in $\Gamma$. See, for example, Programming ...
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0answers
136 views
How can I find the PhD thesis of A. V. Kostochka?
I've searched for the doctoral thesis of Alexandr V Kostochka in internet but couldn't find it. Can somebody help me?
I have searched in his publications list (which contains only one article ...
4
votes
0answers
86 views
Complexity of inclusion of transfinite expressions
Transfinite expressions on an alphabet $\Sigma$ are generated by the grammar :
$$e,f:= a\in\Sigma\mid e\cdot f\mid e+f\mid e^*\mid e^\omega.$$
They describe languages of transfinite words, i.e. words ...
1
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0answers
37 views
Full version of the paper "Characterization of Temporal Property Classes"
Look at this paper:
E. Chang, Z. Manna, A. Pnueli.
"Characterization of Temporal Property Classes"
The proof of Theorem 8 at page 8 says: "We will outline the proof which appears in the ...
2
votes
2answers
112 views
Translation of Counter-free automata into Linear Temporal Logic
There is a well-known equivalence between counter-free automata and Linear Temporal Logic (which is cited for example by [1]). However, I cannot find a concrete way to obtain an LTL formula from a ...
0
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0answers
66 views
"Fast" approximation algorithm for geometric hitting set of same-height rectangles
In the Geometric Hitting Set problem, we are given a set of $m$ geometric objects and a set of $n$ points in $\mathbb{R}^2$, and we wish to find a small subset of the points that hits all the objects.
...
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99 views
Can the rendezvous problem be solved without exploration in synchronous rings?
Problem Definitions:
Rendezvous: A number of agents, in this case two, that start from distinct nodes of a ring need to meet in some node that is not known in advance.
(Collaborative) Exploration: A ...
3
votes
1answer
149 views
TSP with "enemy" nodes
I am curious if the following variation of the traveling salesman problem (TSP) (or a vehicle routing problem (VRP) version) occurs in the literature and has a name I could search for.
The story/idea ...
1
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0answers
38 views
program search with optimization methods for (resource bounded) Kolmogorov complexity
Are there fields of research that look at finding short programs for generating strings (therefore trying to find the (resource bounded) Kolmogorov complexity of the string), but using optimization ...
1
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0answers
50 views
sophistication or logical depth to detect intelligent extra-terrestrial species
From my understanding, Algorithmic information theory (AIT) gives some ways to define the amount of « structure » in a string: for example sophistication or logical depth (see for instance [1]), can ...
3
votes
1answer
101 views
Hardness when restricted to an infinite number of far apart instance sizes
Is there a result that rules out (under common complexity theoretic assumptions) that one can solve an NP-hard problem in polynomial time for an infinite number of possibly very far apart instance ...
0
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1answer
89 views
Reference for context-free grammar for Martin-Löf type theory
Are the terms and the types of Martin-Löf type theory described by context-free grammars? Have such grammars been written down somewhere?
7
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0answers
149 views
Where is Yao's original proof that distinguishers imply next-bit-predictors?
In the theory of pseudorandomness, there is a well-known lemma that says roughly the following. Let $X$ be a probability distribution over $\{0, 1\}^n$. Suppose there is an efficient algorithm that ...
3
votes
1answer
255 views
Proof and computational complexity
I couldn't find documents elaborating on this: if the Curry Howard correspondence is to be interpreted as establishing a strong relation between proofs and programs, should there not be a strong ...
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0answers
36 views
What is known about the stabilizer rank of this simple state?
Consider the uniform superposition of all length-$n$ bit-strings of Hammming weight $w$,
$$ |\phi_w\rangle =\sum_{x\in \{0,1\}^n,|x|=w} |x\rangle$$
What is known or conjectured about the stabilizer ...
0
votes
1answer
70 views
Given a partition and an element, find the subset that includes this element
I am interested in the following simple problem: Let $X$ be a set and $X_1\cup X_2\cup\cdots\cup X_k$ be a finite partition of $X$. Given $x\in X$, find the subset $X_i$ for which $x\in X_i$. I am ...
4
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0answers
67 views
Terminology for languages of pairs of words
I want to consider $L \subset A^* \times B^*$ as a "language". Is there standard terminology for this?
I wrote "double language" first (but that doesn't sound right to me), then &...
3
votes
1answer
97 views
Approximating Independent Dominating set on bipartite graphs
I'm interested in the following problem: given a bipartite graph, find the smallest independent set of vertices which dominate all other vertices.
My question is: are there any positive results in the ...
3
votes
0answers
62 views
Multi-round communication complexity of greater than
For the "greater-than" problem in Yao's 2-party communication complexity model, Alice receives $X$ and Bob receives $Y$, and they need to decide whether $X>Y$.
I recently listened to an (...
7
votes
1answer
395 views
Strongly normalizing type theory beyond induction-recursion
Are there known type theories in the literature, which have strong normalization proofs and their proof-theoretical strength goes beyond strength of type theories with induction-recursion?
4
votes
0answers
80 views
Relative consistency of various Martin-Löf style type theories
I am wondering about relative consistency of various Martin-Löf type theories, when compared to one another, I will use MLTT for the intensional Martin-Löf type theory with $\Pi$, $\Sigma$, $\mathbb{N}...
1
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2answers
105 views
Name of this graph partitioning problem? (related to coloring)
Given a graph $G=(V,E)$ and an integer $k$, find a partition $P_1, P_2, \dots, P_k$ of $V$ into $k$ parts that minimize the total number of edges between two vertices in the same part, i.e. $\sum_i |(...
4
votes
0answers
104 views
Trading treewidth for depth in Boolean circuits
We know that languages defined by (poly-sized) Boolean formulae equals $\mathbf{NC}^1$: that Boolean formulae can be simulated in $\mathbf{NC}^1$ was shown by Brent/Spira [B,S], and the converse is ...
4
votes
2answers
255 views
Density of semantics in syntax
Let $L$ be a programming language, and $\cong$ a notion of equality of $L$-programs (in general $\cong$ will be undecidable). Let $syntax(n)$ be the number of $L$-programs of size $n$ (for some ...
7
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0answers
156 views
A variant of transfer learning
Suppose we want to train $K$ linear classifiers based on iid samples. Each classifier is of the form
$x\mapsto\mathrm{sign}(w\cdot x+\theta)$, with the constraint that the hyperplane $w$ is the same ...
0
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0answers
25 views
Given an input sequence of real numbers, how to find the closest sequence in a large set of sequences
We are given a set $S$ of $m\gg 1$ sequences (arrays) of $n$ elements, where each sequence $s\in S$ belongs to $\mathbb{R}^n$.
In the problem I am trying to solve, in a sequential fashion, we obtain a ...
