Questions tagged [reference-request]
Reference-request is used when the author needs to know about work related to the question.
1,534
questions
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Structural normalization algorithm for the simply typed lambda calculus
I would like to know if there is a (piecewise) structural normalization algorithm for the simply typed lambda calculus. By structural I mean a recursive function that only calls itself on subterms of ...
6
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2
answers
405
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Complexity of Unknotting problems
The complexity of the Unknotting problem is known to be in $\mathrm{NP} \cap\mathrm{co\text-NP}$, see references:
The Computational Complexity of Knot Problems.
Knottedness is in NP, modulo GRH. .
...
3
votes
0
answers
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Hessian of non differentiable convex function
The motivation of the question is the following:
Let $P$ be a set of $n$ points in $\mathbb{R}^d$. Consider the following objective(convex and differentiable) function $f:\mathbb{R}^d\rightarrow [0,\...
0
votes
0
answers
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A variant of randomized co-ordinate descent
Let us consider the following optimization problem.
$\mathcal{P} =\{P_1,\cdots,P_n\}$, where $P_i\subset\mathbb{R}^d$. Let $m = max_i\lvert P_i\rvert$. The goal is to find a point $c$ such that ...
6
votes
2
answers
287
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Intuition behind nested positivity and counterexamples
I'm looking at the nested positivity conditions for inductive types stated in the Coq manual. First off, are there any other references (not necessarily for Coq, but in dependent type theories ...
4
votes
1
answer
135
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Survey on Quantum error correction
Are there any standard recent survey articles on quantum error correction (and may be including fault Tolerant computing)? The most standard ones that many people refer to are this and this. Both of ...
13
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2
answers
589
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One-way randomized communication complexity of Greater-Than
Let $\mathrm{GT}_n:\{0,1\}^n \times \{0,1\}^n \to \{0,1\}$ be the greater than function: $\mathrm{GT}_n(x,y)=1$ exactly when the positive integer whose binary representation is $x$ is greater than the ...
4
votes
1
answer
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Survey on Erdős-Pósa?
Does anyone know of any good surveys on Erdős-Pósa?
I am particularly interested in what are the latest results for the bounding function for directed and even cycles in planar and minor free graphs ...
2
votes
1
answer
90
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"Parity testing set" for disjoint pairs of sets
I'd like a construction of the following description. Let $V$ be a set of $n$ elements. I'd like a collection $X$ of subsets of $V$ such that for any pair $(P,Q)$ of disjoint subsets of $V$, there ...
1
vote
2
answers
181
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Can concurrency models be compared in terms of some metrics?
In Seven Concurrency Models in Seven Weeks by Butcher, it compares Actor Model and Communicating Sequential Processes (CSP):
CSP is more flexible than actor model:
In actor model, the medium of ...
0
votes
1
answer
131
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Generalisations of the Fundamental Theorem of Statistical Learning to different tasks and losses
The fundamental theorem of statistical learning gives an equivalence between uniform convergence of the empirical risk to learning in the PAC framework.
I have only seen this stated in the case of ...
0
votes
1
answer
160
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Upper bound on Independence Number of Random Regular Graph with degree $\Theta(\sqrt{|V|} \log^2 |V|)$
Let $G=(V,E)$ be a random $\Delta$-regular graph with $\Delta \in \Theta(\sqrt{|V|} \log^2 |V|)$. I'm analysing an algorithm having asymptotic running time crucially depending on the Independence ...
1
vote
1
answer
216
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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(...
3
votes
0
answers
96
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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 ...
7
votes
1
answer
118
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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 $\mathcal{C}$;
...
6
votes
0
answers
158
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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 ...
12
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0
answers
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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
1
answer
142
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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
2
answers
183
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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
1
answer
298
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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 ...
1
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0
answers
39
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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
1
answer
130
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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
0
answers
158
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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 ...
3
votes
1
answer
198
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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
2
answers
286
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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 ...
4
votes
0
answers
80
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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
1
answer
279
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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
0
answers
152
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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
0
answers
93
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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 ...
3
votes
1
answer
141
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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
0
answers
51
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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
0
answers
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
1
answer
96
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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
0
answers
54
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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
0
answers
163
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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
0
answers
77
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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
0
answers
159
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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
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0
answers
77
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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, ...
2
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1
answer
292
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How can I find the PhD thesis of C.A. Ellis?
I've searched for this article all over the web but couldn't find it. can anyone help me?
Ellis, C.A. 1969. Probabilistic languages and automata. Rept. no. 355. Dept. Comp.
Sc. University of Illinois, ...
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0
answers
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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 ...
4
votes
0
answers
103
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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
2
answers
109
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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
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1
answer
236
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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
1
answer
144
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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
1
answer
88
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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
1
answer
242
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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-...
14
votes
3
answers
477
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"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 ...
9
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2
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635
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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 $...
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votes
2
answers
367
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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
1
answer
139
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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 ...