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0
votes
1answer
116 views

Finding top-K items in a sliding window

Imagine we have a stream of bank transactions. Each transaction has a target account and some amount of money. I'd like to find top K accounts over some period of time (e.g. last 7 days) which ...
2
votes
2answers
114 views

Information and Coding Theory Texts

I am coming from a pure mathematics (in analysis) background and am curious to learn some information and coding theory. I am after some recommendations on texts. Due to my personal background I am ...
3
votes
1answer
74 views

Recursive generic oracles

In Fenner, Stephen; Fortnow, Lance; Kurtz, Stuart A.; Li, Lide, An oracle builder’s toolkit, Inf. Comput. 182, No. 2, 95-136 (2003). ZBL1025.68041, the authors go through a variety of generic oracles. ...
6
votes
5answers
294 views

Relationship between Random Graph Theory and TCS

Sorry for this large and vague question. I am a new grad probability student recently interested in random graph theory(RG). I heard from someone in math department that RG has close relationship to ...
0
votes
1answer
35 views

Are perceptual hashes connected to audio/video compression?

Without loss of generality, I'll only talk about video, but this should apply to any sort of signal. A perceptual hash function (WP) maps videos to fingerprints such that each fingerprint's preimage ...
0
votes
1answer
125 views

What is a known sequence for which being constant is not provable?

My question concerns the property of being constant for computable functions ${\mathbb N}\to \{0,1\}$, within any common framework $T$ strong enough to include Heyting arithmetic (and of course not ...
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 $C|0,0,...,0>$. ...
1
vote
1answer
102 views

Lower bound for proving a random 3-SAT formula is unsat?

For a random 3-CNF formula with n variables and m clauses, assume this formula is unsat, what is the lower bound for proving it to be unsat? Some results posted in Lower bounds for random 3-SAT via ...
1
vote
0answers
147 views

Is polynomial-time the same in all classical computational models?

There are many models of computability, all giving the same notion of 'computable function'. To pick a few examples: Turing machines (with variants: one-ended, two-ended, multiple tapes...) RAM ...
1
vote
1answer
81 views

Are coproduct types redundant in presence of natural numbers and $\Sigma$-types?

In the homotopy type theory book section A.2.5 defines $\Sigma$-types, A.2.6 coproduct types and A.2.9 the natural numbers type. If we already have $\Sigma$-types and the natural numbers type can we ...
6
votes
0answers
140 views

Fastest exact algorithm for MAXCUT

Is the algorithm introduced in the following paper still the fastest exact algorithm for general MAXCUT problems? TIA Ryan Williams, A new algorithm for optimal $2$-constraint satisfaction and its ...
7
votes
1answer
179 views

What is the complexity class of higher-order primitive recursion?

Short and sweet: The complexity class of primitive recursive functions (WP) is PR (WP, Zoo). What's the complexity class of higher-order primitive recursion (WP)? The motivating context is simply that ...
4
votes
2answers
224 views

Complexity of "can we get a cycle by stacking directed bipartite graphs?"

Preliminaries We consider directed bipartite graphs of the form $G = (V,V',E)$, in which the nodes are partitioned into $V = \{1,\ldots,n\}$ and $V'=\{1',\ldots,n'\}$, with $|V|=|V'|=n$, and $E\...
0
votes
0answers
51 views

Number of composite factors as a function of the number of bits of an integer

Is there a standard formula to calculate the number of composite factors using the number of bits of an integer?
0
votes
0answers
42 views

Using bin-packing algorithms to approximate maximum-makespan

Bin-packing (BP) and maximum-makespan (MM) are dual problems. In both problems, the input can be defined as a set $S$ of positive integers, and the output is a partition of $S$. In BP, there is a ...
15
votes
6answers
5k views

Can theoretical computer science be applied in social sciences?

I'm very new to this field - technically not in it but want to be. I'm very early in my academic career (sophomore at a community college) but decided that I want to add a math major along with my ...
1
vote
1answer
135 views

Is QMA known to contain Co-NP?

Is QMA known to contain Co-NP? If not, would Co-NP being contained in QMA have any implications for other complexity classes. (e.g. Causing the polynomial heirachy to collapse.)
2
votes
1answer
164 views

A variant of two-counter machine

I would like to show that the halting problem for some variant of two counter machine (Minsky machine) is undecidable: instead of "if c=0 goto i else goto j", there are "if c>d goto ...
0
votes
1answer
157 views

Lexicographic Boolean satisfiability

Maximal Satisfying Assignment (Lexicographic Boolean satisfiability / LexMaxSAT), the problem of finding the lexicographically maximum x_1, . . . , x_n ∈ {0, 1}^n that satisfies Boolean formula φ, or ...
0
votes
0answers
34 views

Bin Packing And Preemptive Multi-Core Scheduling

I am trying to solve a preemptive multi-core scheduling problem, where the input is the tasks. The number of cores M can be decided after seeing the input tasks. I ...
1
vote
1answer
92 views

Partition the edges of a bipartite graph into perfect $b$-matchings

Any $r$-regular bipartite graph can be partitioned into $r$ disjoint perfect matchings. I want to know whether a version of this extends to perfect $b$-matchings. Suppose we have a bipartite graph $G =...
0
votes
0answers
95 views

Questions about the equivalence between PH and depth-d circuits with respect to an oracle

Consider an oracle $A$ and the language \begin{equation} P(A) = \{x\in \{0, 1\}^{n}: \text{the number of strings in }~A~\text{of length}~|x|~\text{is odd}\}. \end{equation} I am trying to make sense ...
6
votes
1answer
217 views

What is the impact of encodings of sparse structures on the complexity of the model checking problem?

Some preliminaries first. Consider a purely-relational structure (a.k.a. database) $\mathfrak{A} = (A, R_1^{\mathfrak{A}}, \ldots, R_{|\tau|}^{\mathfrak{A}})$ over some finite signature $\tau = \{ R_1,...
7
votes
0answers
157 views

$\lambda$-definability and structure preserved by homomorphisms

I imagine there are some standard results that bear on this, but I'm having trouble finding a proof or refutation of it. Some prelimary definitions. A Henkin structure $A = (A^\cdot, ⟦\cdot⟧_A)$ for ...
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,\...
2
votes
0answers
83 views

Resource on phase transition in MAXCUT problems

Could anyone suggest reading materials on phase transition in MAXCUT problems other than [1]? Thanks. Ref: Coppersmith, Don, David Gamarnik, Mohammad Taghi Hajiaghayi, and Gregory B. Sorkin. "...
0
votes
1answer
86 views

Max-k-cut with negative edge weights

Let $G=(V,E,w)$ be a graph and for edge $e\in E$, there is associated weight $w_e$. The max-k-cut wants to partition V into k subsets $P_1,\cdots,P_k$ and maximize $\sum_{1\leq r<s\leq k}\sum_{i\in ...
1
vote
0answers
72 views

BCH codes and polynomials with many values in a subfield

For points $P=\{x_1, \ldots, x_n\} \subset {\mathbb F}_{2^m}$ define $$\mathcal{C}(P, t) =\{(f(x_1), \ldots, f(x_n)) \mid \mbox{$f\in {\mathbb F}_{2^m}[X]$ has degree $t$}\}$$ and $\mathcal{C}'(P, t) =...
-3
votes
1answer
104 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 ...
1
vote
1answer
46 views

Graph classes where giving a q-clique edge cover makes testing for q-colouring easy

A $q$-clique of a graph is a complete subgraph on $q$ vertices. A $q$-clique edge cover of $G$ is a set of subgraphs of $G$ such that each subgraph is a $q$-clique and each edge of G is contained in ...
1
vote
0answers
42 views

Prune length distribution of random binary tree

Consider a random binary tree with $N$ leaves. Each node (except the root node) has a degree of exactly three (two children and one parent). No further restriction is placed on the structure of the ...
0
votes
0answers
49 views

Is p-dimensional matching with (p−1)n edges NP-hard? What about 3n edges?

Let $p≥3$ an integer. I am wondering whether or not the following problems are NP-hard or not (and if they are, I am looking for a convincing argument, or even better a detailed proof): Let $V_1,\...
-1
votes
1answer
95 views

Why structural rules define the "smallest relation" satisfying the rules? [closed]

I'm following a university course based on these slides, and I have a question about structural operational semantics. As you can see at page 7 (4-th slide), a structural rule is interpreted logically ...
3
votes
1answer
96 views

Finding the single-crossing embedding of a single-crossing graph

Is it known how to find a (piecewise) straight-line embedding of a single-crossing graph on the plane with exactly one crossing in polynomial time? We are currently trying to come up with a method for ...
7
votes
2answers
276 views

What's the categorical semantics of definitional equality?

The categorical semantics of a dependent type theory is normally described as a CwA/CwF/CompCat/etc. and in these models, we can talk about propositional equality by interpreting an 'identity type'. ...
7
votes
0answers
282 views

Problem in the paper "Stable Minimum Space Partitioning in Linear Time"

The paper Stable Minimum Space Partitioning in Linear Time describes an algorithm that stably sorts a binary array (an array whose elements can only have two distinct values) in $O(n)$ time complexity ...
4
votes
0answers
122 views

An NP-hard Hidden Subgroup Problem

I've encountered a model which can be thought of as a version of the Hidden Subgroup Problem (https://en.wikipedia.org/wiki/Hidden_subgroup_problem), but that doesn't quite meet the standard problem's ...
0
votes
0answers
15 views

Linear auto-encoders and PCA with unequal input-output

It is a well-known fact that linear auto-encoders are equivalent to PCA, i.e. for the data matrx $X\in {\mathbb R}^{n\times N}$ the task $$ \min_{W\in {\mathbb R}^{n\times k}}||X-WW^TX|| $$ has a ...
4
votes
1answer
190 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
0answers
75 views

"Search and Replace" Edit Distances

Which results are known about the string edit distances using the edition operator "Search and Replace"? Edit distances were traditionally used in bio informatics and to correct ...
0
votes
2answers
149 views

An (unusual?) risk bound

I am told that that a bound on the generalization error of the following form exists in terms of something called the ``shattering coefficient" - but I am not able to reference this quantity in ...
0
votes
1answer
114 views

Does an upper bound on the integrality gap imply an approximation algorithm with the same ratio?

Often, we can model combinatorial optimization problems with an Integer Program. Then there is an associated Linear Relaxation which drops the integrality constraints on the variables. Let's say we ...
1
vote
0answers
87 views

Where does "Quine's Method" in propositional logic originate?

Hein (407-408) states that Quine's method "...uses these (14) properties together with basic equivalences to determine whether a wff is a tautology, a contradiction, or a contingency." The ...
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 ...
0
votes
0answers
57 views

Examples of SDP constant approximation algorithms on minimisation problems

I was recently going through a survey on semidefinite programming and its use in approximation algorithms. Here are some problems I am familiar with that have SDP approximations: Max Cut ($\approx 0....
2
votes
1answer
152 views

Minimum cut with size bounds $k\leq |S| \leq |V|-k$

It is known by the max flow min cut theorem that the minimum cut problem is in $P$. I am interested in knowing what is known on the complexity of the minimum cut with size $k\leq |S| \leq , |V|- k$. ...
1
vote
1answer
165 views

Can you embed a Turing Machine into the Pi calculus with just one replication operator?

See title. If it is not universal, then how is the power of the pi calculus with this restriction characterized?
1
vote
0answers
66 views

What is this structure? (monad with a kind of partial inverse comonad)

I have encountered a structure that looks like a monad with a one-sided inverse and some additional properties. I am not sure which properties of this structure are essential and which are accidental, ...
1
vote
0answers
49 views

Failing to understand a lemma regarding Robust Low Rank Approximation

I am reading Low Rank Approximation in the Presence of Outliers by Bhaskara and Kumar and kind of stuck at the proof of Lemma 9. The paper studies robust (to outliers) low rank approximation problem. ...
6
votes
3answers
1k views

How does type theory change how one thinks about programming?

I have been dabbling in HoTT and I am convinced that dependent type theory is much more suitable than set theory for proof assistants. Now, this made me wonder - how fundamental is Type Theory ...

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