# Questions tagged [reference-request]

Reference-request is used when the author needs to know about work related to the question.

1,425 questions
Filter by
Sorted by
Tagged with
65 views

### 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 ...
46 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?
37 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⁡(...
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 ...
99 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 $\mathcal{C}$; ...
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 ...
147 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 ...
84 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 ...
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 ...
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 ...
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 ...
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: ...
331 views

### Major open problems on polynomial kernel (non) existence

We are not able to settle the (non-)existence of a polynomial kernel for a parameterized combinatorial NP-complete problem (we also tried to apply some recent lower bound techniques to prove the non-...
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 ...
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 ...
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?
407 views

### Are there protein-based computational models?

Is there a framework/formalism that defines computational models based on proteins other than Adleman's DNA model or this work by Cherry and Qian? Edit 2020 (related models/ideas based on DNA): DNA ...
450 views

### Boolean formula balancing in $\mathsf{AC^0}$

I am looking for references about the complexity of Boolean formula balancing problem. In particular, Was it known that Boolean formulas can be balanced in $\mathsf{AC^0}$? Is there a simple proof of ...
109 views

### Metrics for modelling convergence in the lambda-calculus

I wonder if there have been efforts to reconcile the measure approach to termination and Scott's domain theory or other topological models of computation. In other words, can we translate this measure ...
397 views

### Algebraic topology for termination proofs

I'm reading about various ways in which termination proofs of software verifiers are built: ad-hoc methods that detect recursions, term-rewriting, synthesis of lexicographic orderings... From the ad-...
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 ...
245 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 ...
98 views

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 ...
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 ...
209 views

### A Simple Auction Game

You are playing the following game. You have a budget of $B$ dollars. There are $n$ days. Every day $d$, you have to make a bid $b_d\geq0$ that does not exceed your budget. After making the bid, a ...
3k views

### computing the minimal NFA for a DFA

Many years ago I heard that computing the minimal NFA (nondeterministic finite automaton) from a DFA (deterministic) was an open question, as opposed to the vice versa direction which has been known ...
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 ...
8k views

### Examples of the price of abstraction?

Theoretical computer science has provided some examples of "the price of abstraction." The two most prominent are for Gaussian elimination and sorting. Namely: It is known that Gaussian elimination ...
140 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.
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 ...
119k views

### What Books Should Everyone Read?

[Timeline] This question has the same spirit of what papers should everyone read and what videos should everybody watch. It asks for remarkable books in different areas of theoretical computer ...
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 ...
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, ...