Questions tagged [reference-request]
Reference-request is used when the author needs to know about work related to the question.
1,424
questions
0
votes
1answer
26 views
VC-dimension of infinite set of triangle wave
I am searching for the VC-dimension of the following:
What is the VC-dimension of the infinite set of triangle wave functions with
amplitude 1 and period parameter p on points on the line?
2πarcsin(...
-1
votes
0answers
36 views
VC-dimension of a ball [closed]
I am searching for the VC-dimension of the following:
What is the VC-dimension That can ball (3D) can shatter in 3 dimension?
1
vote
0answers
64 views
Request for an update on a discussion about coinductive types in HoTT (or anywhere else)
Googling something else I stumbled on a conversation titled "coinductives" initiated by Vladimir Voevodsky on Google groups in 2014. It lasted for three days, invloved a dozen people, and ...
6
votes
1answer
98 views
Extending cographs with product operation
Let $\mathcal{C}$ be the class of undirected graphs defined inductively as follows:
A single vertex is in $\mathcal{C}$;
If $G\in\mathcal{C}$ then its complement $\overline{G}$ is in $\mathcal{C}$;
...
4
votes
0answers
78 views
Computing and maintaining the minimum of a set $S$ of integers while allowing updates on $S$
This question is about computing and maintaining the minimum of a set $S$ of integers while allowing updates on $S$.
The computation model we are considering is the unit-cost RAM machine with linear ...
11
votes
0answers
145 views
Regular languages accepted by an automaton with at most one transition per letter
I'm interested in the (very restricted) subset of regular languages for which there is an automaton having the following property: for every letter $a$ of the alphabet, the automaton has at most one ...
3
votes
1answer
83 views
Generalizations of Dyck languages?
The "narrowest" generalization of Dyck languages that I am aware of is Visibly Pushdown languages. Are there any useful classes of languages that are intermediate between Dyck languages and ...
2
votes
2answers
137 views
A clear and rigorous explanation of critical pairs and the Knuth-Bendix completion algorithm?
I'm looking for an explanation of critical pairs and the Knuth-Bendix completion algorithm that is at once rigorous and of high pedagogical value, i.e. clear, detailed, containing illustrative ...
10
votes
1answer
204 views
The number of clauses in an unsatisfiable CNF
I am interested in generalisations of the following observation:
An unsatisfiable $k$-CNF has at least $2^k$ clauses.
A special case of the observation is when $k=n$, where $n$ is the number of ...
0
votes
0answers
15 views
Notation for scheduling problems with multiple release times/deadline intervals
I am interested in the classical scheduling problems where we are given jobs with a release time and a deadline, we must find a schedule for all jobs. Specifically, I am interested in the variant ...
1
vote
0answers
28 views
Nominal Tree Languages i.e. with Binders and Infinite Symbols?
I'm wondering if there has been any research done into automata that accept languages of trees that can bind arbitrary variables, and are considered equal under alpha equivalence.
I've found so far:
...
3
votes
1answer
112 views
Number of maximal cliques in a ($2C_4$, $C_5$, $P_5$)-free graph
So far, I have found out that chordal graphs have linear number of maximal cliques with respect to the number of vertices.
In general case, it is exponential.
I am trying to determine whether the ...
7
votes
0answers
127 views
Reference for computing the rank of a matrix in polynomial time
In a recent paper, I need to use the fact that computing the rank of a matrix over the integers has polynomial complexity. Given the context, I don't particularly care about the exact asymptotics, as ...
1
vote
0answers
76 views
Looking for an online community specializing in the Z specification language, where I can ask questions
Where can I find an online community specializing in the Z specification language, where I can ask specific questions about the ISO standard for Z?
3
votes
1answer
232 views
Entropy-like quantity
For $p\in[0,1]^{\mathbb{N}}$ and $\alpha\ge1$, define
$$ H_\alpha(p) = \sum_{i\in\mathbb{N}}p_i|\log(p_i)|^\alpha.
$$
When $\sum_i p_i=1$ and $\alpha=1$, $H_1(p)$ is just the Shannon entropy of the ...
2
votes
0answers
42 views
Harmonic analysis of sequences of Boolean functions (i.e. of words in $(\{0,1\}^n)^*$)
Is there any research on harmonic analysis of sequences of Boolean functions, which represent the application of a Boolean function on a word in $(\{0,1\}^n)^*$?
I'm looking for any reference on this, ...
7
votes
1answer
244 views
Testing for finite expectation
The mean of a positive random variable $X$ is either finite or infinite; define $J(X)$ to be $0$ in the former case and $1$ in the latter case. Claim: there does not exist a function $J_n$ from the ...
5
votes
0answers
98 views
Exact algorithms for $k$-means
Lets recall the definition of $k$-means clustering for euclidean spaces.
Let $X$ be a set of $n$ points in $R^d$ and $k$ a given natural number. Let $C$ any $k$ clustering of $X$. Define the cost of $...
9
votes
0answers
84 views
Reference request: DFA linear-time minimization
What is the most complicated kind of deterministic finite-state automaton that can be minimized in $O(n)$ time?
Here’s what I’ve been able to find so far:
The acyclic case has been solved. So any ...
2
votes
0answers
65 views
Polynomial convergence to optimal move of the UCT algorithm. Missing proof?
This is a question regarding the theoretical convergence guarantees of the UCT algorithm, a popular variation of the Monte Carlo Tree Search algorithm (used in games, planning, reinforcement learning, ...
1
vote
0answers
44 views
Reference request: algorithm meta-analyses
Could you direct me to papers that survey families of algorithms? The ideal paper would focus on a single family of algorithms, would show how the improvements in each algorithm work, and ideally ...
1
vote
0answers
64 views
Reference to “compressibility” of logarithmic space [closed]
Is there a reference somewhere for the result SPACE($O(\log n)$) = SPACE($\log n$)? i.e. Big-O doesn't matter in logspace since you can compress the space. I feel like this is an elementary result but ...
3
votes
1answer
77 views
Reference request: pi-calculus with simultaneous events
I am interested in using the $\pi$-calculus as a basis for modeling workflows, and came up with an extension that proved useful in my modeling, namely the ability to specify that two or more channel ...
1
vote
0answers
54 views
polytime approximability of directed multicut
Does anyone know how well directed multicut can be approximated in planar and minor free graphs? Also any survey of approximability of directed multicut and multicut in various graph classes would be ...
2
votes
0answers
138 views
Order-invariant conjunctive queries are FO-definable without the order
I'm looking for a reference for Exercise 6.11 from Libkin's FMT book:
Prove that an order-invariant conjunctive query is FO-definable without the order relation.
All help is appreciated.
5
votes
0answers
69 views
Chosen message attack on unhashed GGH signatures?
Background: I've been reading GGH's Public-Key Cryptosystems
from Lattice Reduction Problems, and have a question about a remark the authors make:
"It is important to remark at the outset, that ...
4
votes
0answers
69 views
Best known hidden constant in complexity of AKS sorting networks
The famous AKS sorting network allows one to sort $N$ elements via a circuit composed out of comparator gates, where the circuit has size $\mathcal{O}(n \log n)$ and depth $\mathcal{O}(\log n)$.
The ...
5
votes
0answers
51 views
reference request: greedy algorithm for fractional interval covering
Reference Request
I've found a natural greedy algorithm for the problem below. My question is: what is already known about fast algorithms for this problem (faster than general linear programming, ...
1
vote
0answers
64 views
Reference request on using Kolmogorov complexity to measure the simplicity of models
Have there been any serious attempts to use the notion of Kolmogorov complexity to measure the simplicity of models outside of theoretical CS? I mean models in the english sense - any logical set of ...
3
votes
0answers
83 views
Origin of simulation relations for compiler correctness
Leroy uses simulation relations as a means of showing compiler correctness; the basic idea is that a simulation relation is an asymmetric binary relation between states in two different small step ...
1
vote
2answers
100 views
Where to find info on (polytime) approximability of various discrete optimization problems?
Where to find info on (polytime) approximability of various discrete optimization problems?
Sorry if this is stupid,but is there a site or reference that keeps up to date info on approximability of ...
11
votes
1answer
174 views
Is there a language of first-order logic such that every r.e. set is Turing-equivalent to some finitely axiomatizable theory in that language?
I hope that mathematical logic / recursion theory type questions are welcome here. I am sorry this question is so long and technical, but I believe that if you read it you will find that it is well-...
6
votes
1answer
131 views
Complexity of approximating a real function using queries
Consider the following computational problem, where $I$ is the real interval $[-1,1]$:
There is a monotonically-increasing function $f: I\to I$. You are allowed to access it only through queries of ...
5
votes
1answer
80 views
Complexity of computing the union of H-polytopes in three dimensions
Consider a set $P_1,\ldots,P_k$ of polytopes in $\mathbb{R}^3$, each given as an intersection of halfspaces with rational normals (in particular, they are all convex).
We are also given a target ...
6
votes
1answer
150 views
Good Survey paper for k-means/k-median/k-center/facility-location
I have stated 4 problems in the Question title.
All these problems are closely related and are studied in various variations. For example:
Space: Euclidean/metric/discrete/continuous/non-metric/2-...
13
votes
3answers
365 views
“Refined” list of open problems in TCS
In the conference on learning theory (COLT), a list of open problems is published every year, for example, the list of 2019.
The open problems are being submitted and peer reviewed, which makes this ...
8
votes
1answer
349 views
Can we efficiently enumerate the words accepted by a DFA by order of increasing weight?
Fix a deterministic finite automaton $A$ defining a regular language on the alphabet $\Sigma = \{0, 1\}$, and call the (Hamming) weight of a word $w \in \Sigma^*$ its number of $1$'s. Given a length $...
-2
votes
2answers
151 views
Proof that optimal solutions of LP Relaxation of independent set are half-integral
I saw somewhere that optimal solutions of LP Relaxation of independent set are half-integral, by what I mean the possible values of a solution are ${ \{0,0.5,1 \} }$. I'm looking for proof of that.
...
1
vote
1answer
117 views
Diagonalization arguments for QMA type proof systems
Diagonalization is a very common technique to find oracle separations. For example, it can be used to separate $\cal{P}$ and $\cal{NP}$, with the essential idea being that of constructing an oracle in ...
4
votes
1answer
124 views
Citation for isometric embeddability of $\ell_2$ into $\ell_p^\binom{n}{2}$ for $p \geq 1$?
I need to use the following well-known result in my paper:
Let $X$ be a set of $n$ points in $\mathbb{R}^d$. Then $(X,\ell_2^d)$ embeds isometrically in $\ell_p^\binom{n}{2}$ for all $p \geq 1$.
...
1
vote
0answers
69 views
Hardness of vertex colouring on hypergraphs with $O(\log n)$ edges
I'm interested to know whether there has been any work done on the problem in the title. For the problem to be meaningful, we would naturally need that the hyperedges must have large ($\omega(1)$) ...
1
vote
1answer
67 views
How can I find dependent rounding procedures with the desirable properties?
I'm seeking for materials on dependent rounding. However, what I've found are two papers:
Gandhi, R., Khuller, S., Parthasarathy, S., Srinivasan, A., 2006. Dependent rounding and its applications to ...
4
votes
0answers
105 views
Network design with reachability pattern
We are given two sets of terminals $A$ and $B$. For each $a\in A$, we are also given $R_a\subseteq B$. Let $|A|+|B|=n$.
We want to find a directed acyclic graph $G$ where $A$ and $B$ are subsets of ...
9
votes
4answers
1k views
How do conference proceedings add to academic prestige?
I come from mathematics and, for whatever reason, am trying to publish in theoretical computer science. I'm still trying to understand the role of conference proceedings, and I have two specific ...
2
votes
1answer
198 views
Is $\{0,1\}$-Vector bin packing NP-Hard when vectors have constant dimension?
The paper https://cs.brown.edu/people/seny/pubs/vbponline.pdf discusses $\{0,1\}$-Vector Bin packing in the online setting and give lower bounds. However, they do not mention anything about the ...
7
votes
1answer
163 views
Complexity class of efficient streaming algorithms
Consider the class of problems $\mathsf{StreamL}$ which can be solved in logarithmic space reading the input in a single pass from left to right. In other words:
$L \in \mathsf{StreamL}$ if there ...
6
votes
3answers
452 views
Reference Request: Computational Learning Theory
Pretty soon I will be finishing up Understanding Machine Learning by Shai Ben-David and Shai Shalev-Shwartz. I absolutely love the subject and want to learn more, the only issue is I'm having trouble ...
3
votes
1answer
130 views
What is FO(REGULAR)? (The descriptive complexity equivalent of NC1)
According to Immerman's Descriptive Complexity diagram, there is a logic called $\mathsf{FO(REGULAR)}$ which captures $\mathsf{NC}^1$. However, I can't find the reference where this logic is defined. ...
0
votes
1answer
122 views
Automatic theorem prover for first-order logic versus model checker
What's the formal difference between a model checker, and an automated theorem prover for first-order logic, i.e. something like Meson/Metis/Sledgehammer/Vampire/E? Link to a clear discussion of the ...
0
votes
1answer
83 views
Finding the size $k$ subset in a metric space that maximizes the min distance between elements
I have a metric space $(X,d)$ and I'd like to find a subset of size k of far away elements.
We can cast this as the following optimization problem $\max_{S \subseteq X, |S| = k} ( \min_{i \not = j, ...
