All Questions

5
votes
1answer
65 views

Pop desired elements on stacks of bounded capacity

Consider there are $k$ stacks containing a total of $n$ elements. Each element is either red or blue. We have complete knowledge of each element's location and color. Only push and pop are allowed on ...
7
votes
0answers
114 views

Can relativization technique be applied to natural NP-complete languages?

Levin [1] defined distNP is the distributional problem (L,D), where L ∈ NP, and D is an ensemble of efficiently samplable distributions over problem instances. We say that a distNP problem (L,D) is ...
1
vote
0answers
43 views

Are there any continuous-time stochastic processes in which transition probabilities are discontinuous functions over time? [closed]

In stochastic processes, like homogeneous Markov processes, Poisson processes, Queueing systems etc., the functions that represent (transition) probabilities are continuous over time. This is also ...
2
votes
1answer
201 views

Deciding whether a graph contains a complete balanced bipartite graph

Is it known whether the following problem is in P or is NP-complete? Problem: given an input graph $G$ on $n$ vertices, decide whether $G$ contains a complete $n/2 \times n/2$ bipartite graph.
1
vote
0answers
71 views

Complexity of low-rank matrix factorizations with rows in a simplex and outliers

Our goal is to obtain a matrix factorization in form of $M = U V'$, where $U\in\mathbb{R}^{d\times r}, V \in\mathbb{R}^{N\times r}$ and each row of $V$ satisfies $$ \sum_{j}(V)_{ij}=1, (V)_{ij}\ge 0 $$...
3
votes
0answers
73 views

Fixed dimension Linear Integer Programming in $NC$

We know if fixed dimension linear integer programming is in $NC$ then integer $GCD$ is in $NC$. Is this the only non-trivial implication of fixed dimension linear integer programming in $NC$?
-1
votes
1answer
59 views

Formally prove that the loops of this sorting algorithm will terminate [closed]

Given is the sorting algorithm Bubblesort ...
4
votes
1answer
86 views

Stable order on binary strings

I need some order on binary strings such that if I have a small (but superlinear in their length) number of sufficiently different strings, the order will stay the same if I change a few bits in the ...
4
votes
1answer
143 views

Newman's lemma for distributional communication complexity

This may be obvious — sorry if it is. Newman's lemma (Newman91] shows that any public-coin communication protocol to compute a Boolean function $f\colon \{0,1\}^n\times\{0,1\}^n\to\{0,1\}$ can be ...
0
votes
1answer
63 views

Is a reference on T a subtype of T?

If I take the book Practical Foundations for Programming Languages by Robert Harper, the following definition is given for subtyping: A subtype relation is a pre-order on types that validates the ...
1
vote
0answers
36 views

Back-propagation for computing derivative of certain line integral

Consider a function F (think of neural networks) with two sets of parameters: (1) model parameters $\mathbf{w}$, and (2) input data ${\bf x} \in {\mathbb R}^d$. Fix $i \in [d]$, consider the following ...
1
vote
0answers
35 views

Best approach for allocation problem

I am a bit rusty on optimization algorithms and need an advice. This is my problem: I have n images (with width and ...
1
vote
0answers
267 views

EXPSPACE proof and its implications

I'm dealing with the min-max regret 0-1 Integer Linear Programming problem (MMR-ILP, for short), which is formulated as below. \begin{equation} \label{eq:nip_obj} \min_{x \in \Phi} \sum_{i = 1}^n ...
4
votes
1answer
136 views

Complexity of Acyclic Hypergraph Isomorphism

It is well known that the graph isomorphism problem restricted on trees is much easier than the general case. It can be done in logarithmic space (Jenner B, Lange KJ, McKenzie P. "Tree isomorphism and ...
4
votes
2answers
134 views

Are there hypothesis classes that are hard to learn but easy to test?

Let $H$ be a binary hypothesis class, it is easy to see that if $H$ is (efficiently) properly PAC learnable then it is also (efficiently) testable (here we use the standard notion of within or $\...
7
votes
1answer
176 views

Distinguishing a biased coin with a small set of tests

Say we have a "coin" $f : [n] \to \{\pm 1\}$ so that either $f$ is balanced, or $f$ is $\epsilon$-far from being balanced. It's a classic result that sampling $O(1/\epsilon^2)$ random points of $f$ ...
1
vote
1answer
129 views

Is this a knapsack problem?

I have a set of $K$ keywords. Each of this keywords can have a set of bids from $1\$,\ldots, N\$$. For each bid for a keyword, it will get a specific amount of clicks and a specific cost. Clicks and ...
6
votes
2answers
275 views

Is getting post-doc difficult in theoretical computer science with few published papers? [closed]

I am a Ph.D student ( expected to graduate in few months ) works in computational mathematics. In my PhD, I have published just couple of research papers. I am willing to go for a post-doc( US, Europe,...
0
votes
1answer
131 views

Subset Sum Problem and hard looking instances that are not really hard

I have been working in a subset sum solver (some new approach) and while working on the time complexity analysis I found what I describe below. Maybe this could explain why some "hard looking" ...
7
votes
2answers
192 views

Is uniform convergence faster for low-entropy distributions?

Let $\mathcal D$ be a probability distribution on $\{0,1\}^d$. Let $X_1, \cdots, X_n \in \{0,1\}^d$ be i.i.d. samples from $\mathcal D$. Let $\mu \in [0,1]^d$ be the mean of $\mathcal D$ and let $\...
5
votes
1answer
102 views

Strong Normalization of Extended Calculus of Constructions (CC with cumulative universes)

There are some proofs around to prove the strong normalization of the calculus of constructions (i.e. that all type systems in the lambda cube are strongly normalizing). I have analyzed the proof ...
3
votes
1answer
62 views

Distinguising between the cases of low or high cover number

Is there a known result saying that for some constants $0 < a < b < 1$, it is NP-hard to distinguish a graph having vertex cover number at most $a \cdot n$ from a graph having vertex cover ...
5
votes
1answer
226 views

Evaluation of an arithmetic formula where the time depends on the length of the arguments of gates

Let $(X,+,\cdot)$ be a commutative ring. Let $|\cdot|\colon X\to \mathbb{N}$ be a function that satisfies $|x+y|\leq |x|+|y|$ and $|xy|\leq |x|+|y|$. We call the function length, and length is always ...
1
vote
1answer
109 views

Is balanced Hamiltonian cycle NP complete on maximal plane graphs?

I know that the Hamiltonian cycle is NP complete on the class of maximal plane graphs. If we instead ask about balanced Hamiltonian cycles (i.e. same number of faces on both sides) on maximal plane ...
3
votes
1answer
383 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 ...
2
votes
1answer
111 views

Is there a gap between weak learning and PAC-learning?

For concreteness lets use the definitions of PAC and weak-learning as in the notes of Avrim Blum (http://www.cs.cmu.edu/~avrim/ML12/lect0208.txt) and also his notes on SQ-Learning (http://www.cs.cmu....
1
vote
0answers
43 views

A categorized (?) list of functional pearls in JFP and ICFP

Is there a list of (categorized preferred) functional pearls ever published in ICFP and JFP? I could go to the ICFP proceedings and JFP issues and find all of them, but this would be time-consuming. ...
4
votes
1answer
110 views

Applications of Christol theorem

I'm looking forward to know about applications of Christol theorem mentioned in Jefrrey Shallit's Number theory and formal languages. One of them is purely algebraic: if $f, g \in \mathbb{F}_q[[z]]$ ...
-1
votes
1answer
83 views

When is extra vertex required in arbitrage detection using Bellman Ford?

I am studying applications of shortest path, in particular arbitrage. Specifically, I was reading these two resources: https://stackoverflow.com/questions/2282427/interesting-problem-currency-...
1
vote
1answer
76 views

Pulling a graph across a partition

I am looking for the name for a particular graph property, if it has been studied, and efficient algorithms for computing it, if they exist. I realise that this may be a well known property that I am ...
9
votes
0answers
85 views

Are there cascade decompositions of machines that are more general than finite automata?

The idea of decomposing automata and their associated semi-groups into irreducible sub-components is due to Krohn & Rhodes and has been explored relatively thoroughly. Krohn & Rhodes gave an ...
-2
votes
1answer
201 views

Graduate school for CS theory?

I am currently studying a bachelor's in (joint honours) Mathematics and Computer Science in the UK. I am intrigued by the sorts of problems present in theoretical computer science and I want to ...
1
vote
0answers
103 views

Solving the Halting problem for most inputs [closed]

Is it possible to solve the following version of the Halting problem : given any Turing machine and some input tape, the program should answer if this pair halts or not except possibly for one Turing ...
1
vote
0answers
68 views

Complexity of enumerating over promise problems and circuits?

Given an enumeration over all Turing Machine which run with increasing length, is there a ``complexity class'' which describes the complexity of determining whether a given TM satisfies the promise ...
2
votes
1answer
74 views

Find shortest prefix to generate original string by overlapping

Given a string $S$, I want to find the prefix string $P$ of shortest length, such that the original string $S$ can be generated by concatenating copies of $P$ (where overlapping is allowed). For ...
3
votes
0answers
87 views

Do features always induce a metric?

It is well-known in functional analysis that an inner product always induces a norm and a norm always induces a metric, and the reverse directions do not hold in general. I am wondering if a similar ...
2
votes
1answer
63 views

how to achieve a topological sort of an given sequence with minimum swaps

For example, given the constraints {$a<b,c<d$} and a sequence $[b,a,c,d]$. we just need swap $a$ with $b$ to get an topological sort, I want to ask how to find the sort solutions with minimum ...
1
vote
0answers
77 views

Impartial Combinatorial Games as a core of the final undergraduate project

Solving several problems of Impartial Combinatorial Games in Game Theory has drawn my attention. So that, I'd like to ask if it's possible to use this topic (e.g. Sprague Grundy theorem) as a core or ...
1
vote
1answer
75 views

Cryptography protocols using graph problem instances

I personally am only aware of basic examples of public key cryptography and I haven't studied cryptography yet. I'm curious if there are circumstances in cryptography where using problem instances ...
7
votes
2answers
332 views

Are all turing machines paths predictable?

I was recently studying partial solutions to the halting problem and came across the problem which I discuss below. In particular I was studying when it was computable to tell if a turing machine has ...
2
votes
0answers
48 views

Ordering tours in a Euclidean TSP according to (strictly) increasing length

Let $H$ be the set of all Hamiltonian cycles on the complete graph $K_n$ associated with a set of $n \geq 4$ points $P$ in the plane where edge weights are defined using the Euclidean distance between ...
2
votes
0answers
119 views

Crime prevention using graph theory and machine learning

I am looking for a way to the model the incidence of crime among a network of individuals. Part of it will use machine learning, and part of it will have to resort to some graph theoretic ...
6
votes
1answer
114 views

Time complexity of derivative-based regex matchers

Regex matching using the Brzozowski derivative without any caching or expression-simplifying takes exponential time and space because of the product rule. In Brzozowski's original paper, Brzozowski ...
6
votes
1answer
108 views

About assumptions needed to get convergence of stochastic gradient methods on non-convex objectives

What are the minimal conditions we know of under which we can prove that a stochastic gradient based algorithm can convergence to criticality on a non-convex objective? Are there any necessary ...
1
vote
0answers
49 views

Why do k min-hashes, instead of one hash where we find the k minimum elements?

Traditionally if one wants to sketch streams for Jaccard similarity hashing, one finds the minimum element in each of $k$ permutation for comparison purposes, and then takes number_of_collisions / $k$ ...
1
vote
1answer
153 views

Does every online algorithm has an offline counterpart?

According to the wikipedia page for Online algorithms, it states: "Not every online algorithm has an offline counterpart." At the time of asking this question there is no citation for this claim. ...
4
votes
0answers
88 views

Naming an algorithm after a copyrighted object

In machine learning, it is common to give algorithms quirky names. What happens if you think you've found a name that's actually quite fitting for an algorithm (catchy, descriptive, etc) -- but turns ...
3
votes
0answers
55 views

Problems and theories in CS that uses Fibonacci numbers

I want to know problems and theories where Fibonacci sequence is used and where we have some possibility to use Fibonacci numbers. I have found that- In counting number of steps for Euclidean ...
4
votes
1answer
79 views

What is the current state of the art in black-box grammar induction?

Grammar induction of Context Free Languages seems to be a very well researched field. I would like to know the current state of the art in inducing a Context Free Grammar (I am reading up Higuera's ...
9
votes
2answers
287 views

Hereditary substitution with a universe hierarchy

I've read about hereditary substitution for the Simple Lambda Calculus and for The Logical Framework with distinct terms and types. I'm wondering, are there any examples of hereditary substitution in ...

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