All Questions

0
votes
0answers
26 views

Reference on generalization of plane graph duality between bonds and simple cycles

I've also asked this question on Mathoverflow, but it hasn't gotten an answer after several months: https://mathoverflow.net/questions/316132/reference-on-generalization-of-plane-graph-duality-between-...
2
votes
0answers
78 views

Shortest s-t path when is allowed to ignore k weights

Given an undirected graph $G$ with $n$ vertices and $m$ edges, with non-negative weights on the edges, what's the best algorithm that computes the shortest path from $s$ to $t$, where you are allowed ...
8
votes
2answers
157 views

Intuition Behind Strict Positivity?

I'm wondering if someone can give me the intuition behind why strict positivity of inductive data types guarantees strong normalization. To be clear, I see how having negative occurrences leads to ...
14
votes
0answers
171 views
+100

Perfect matching of monotone Boolean function with null Euler characteristic

For a set $V = \{0,\ldots,k\}$ of variables, let $\mathbf{G}_V$ be the undirected graph with set of vertices $\{S \subseteq V\}$ and set of edges $\{\{S,S'\} \mid S \subseteq S' \text{ and }|S'| = |S|+...
3
votes
2answers
76 views

Compactness of domino tilings

I've read in Lemma 2 of the paper 1 that if every square region of the plane admits a tiling, then the whole plain admits a tiling, but the proof is omitted. This sounds like a compactness property, ...
2
votes
0answers
44 views

Complexity of comparing extended integer power towers

Inspired by this stackexchange question, is it an open problem to compare two power towers of positive integers if we additionally allow numbers lower in the tower to themselves be represented by ...
2
votes
0answers
73 views

Finding 3SUM witness when promised a solution

Suppose we have a 3SUM instance given with the promise that there exists at least one solution. Is the trivial $O(n^2)$ (modulo logarithmic improvements) solution still the best algorithm or is there ...
3
votes
2answers
90 views

Data structure for radial orderings of points on the plane

Assume points are always in general position. For a set of $n$ points $S$ on the plane, a radial ordering with respect to $x\in S$ is a total ordering of the elements in $S-x$. Consider shooting an ...
5
votes
1answer
106 views

What will go wrong if a recursive record type has a negative eta rule?

In the context of Agda like dependent type theory: This short paper https://jesper.sikanda.be/files/vectors-are-records-too.pdf says some inductive type can be seen as records, for example ...
1
vote
1answer
55 views

Complexity status of the Edge Deletion problem to bounded degree graphs

I'm interested in the complexity status of the following problem. Input: a graph $G=(V,E)$ and two natural numbers $k$ and $d$. Output: Yes, if there exists a subset $E' \subseteq E$ of cardinality ...
0
votes
0answers
40 views

Arranging sets in a hierarchy

Suppose you have sets $S_1, \dots S_m$ such that $\sum_i |S_i| = n$. The goal is to arrange all the sets into a (possible unconnected) DAG such that $S_i$ is a parent (or ancestor) of $S_j$ iff $S_j \...
3
votes
1answer
120 views

How small can extension complexity be?

In this article on extension complexity of regular polygons https://arxiv.org/pdf/1505.08031.pdf it is mentioned that extension complexity of $n$ regular polygons should be $\theta(\log n)$. This is ...
3
votes
1answer
135 views

Are Turing machines still useful as model of computation?

Often when I hear "Turing machine," my mind's eye pictures a quaint infinite ticker-tape with a small little machine writing and erasing $0$'s and $1$'s. But when I'm forced to think about a Turing ...
0
votes
0answers
105 views

Canonical complete problem for $\mathrm{FP}^{\Sigma^p_2}$

Given a $\Sigma^p_2$-complete oracle (i.e., $\Sigma_2 \mathrm{SAT}$), I have a problem that requires to call this oracle polynomially many times and returns an integer. Essentially, this is a function ...
1
vote
0answers
66 views

Entropy bounds on solutions to problems in BPP and other complexity classes based on entropy demands

Has anyone studied the asymptotics of problems in complexity classes like $BPP$? The thought came to me that if a problem in $BPP$ only requires $O(log(n))$ bits of entropy to solve then, intuitively, ...
4
votes
0answers
94 views

Arranging letters to make a word in a regular language

Fix a regular language $L$ on the alphabet $\{a, b\}$, and consider the following problem. I am given as input: some number $m \in \mathbb{N}$ of copies of the letter $a$, and some number $n \in \...
4
votes
0answers
81 views

Is there a history-independent rope data structure?

I'm experimenting with a toy (functional) programming language. One of my ideas is to aggressively hash cons everything, thus representing any data structure as a single integer. In that context, data ...
2
votes
0answers
55 views

Partition into c and 1-c

Let $c\in(0,1/2]$ be a constant. Given a set of positive integers with sum $S$, is there a partition into two subsets such that both subsets have sum at least $cS$? If $c=1/2$, this is the famous ...
2
votes
0answers
66 views

how is time complexity defined in computational learning theory

In general, when we say an algorithm $A$ PAC learns $C$ in time $t$, we say $A$ takes time $t$ before outputting a hypothesis $h$, and the hypothesis can be evaluated (on every $x$) in time $t$. Now ...
5
votes
1answer
366 views

What type of mathematical problems interesting for TCS researchers?

I am Ph.D student (about to graduate) in TCS. I have worked on some problems. I have been able to publish few research paper. There are many research problems in mathematics as well in TCS. I am sure ...
-2
votes
0answers
13 views

Quantifying Network Centrality Leader Shift Across Two Networks

I have a Complex Network X, and other Network Y. I calculate Network Centrality measure on each of those networks and rank the top K of them into Leaders_X and Leaders_Y. Network X and Network Y are ...
3
votes
0answers
130 views

Testing emptiness property complexity in Sum of Squares Proof systems

Take the set $$\mathcal T=\{f_1(x_1,\dots,x_n)=\dots=f_m(x_1,\dots,x_n)=0, h_1(x_1,\dots,x_n)\geq a_1,\dots,h_t(x_1,\dots,x_n)\geq a_t\}$$ where $$h_1(x_1,\dots,x_n),\dots,h_t(x_1,\dots,x_n)\in\mathbb ...
5
votes
1answer
84 views

$NP$ completeness of Hamiltonicity of cubic polyhedral plane graphs with bounded face degree?

Let $\mathscr{C}_d$ be the class of cubic 3-connected simple plane graphs, with face degree bounded by $d$. Is there any $d$ such that Hamiltonian cycle is $NP$ complete on $\mathscr{C}_d$? If so, ...
1
vote
0answers
36 views

How to justify this causally consistent execution in the $(vis, ar)$ framework for distributed consistency models?

In Figure 5.1 of the book "Principles of Eventual Consistency" by Sebastin Burckhardt, 2014, Causal Consistency (CC); wiki is (mainly) defined as the conjunction of $hb \subseteq vis$ and $hb \...
6
votes
1answer
249 views

Naive definition of treewidth

Treewidth has arguably pretty involved definition. Recently I was thinking about a problem and turns out it easy to solve it for graphs with small ``naive treewidth''. Naive treewidth is defined as ...
2
votes
2answers
158 views

Extending Hindley-Milner to type mutable references

I have been trying to implement a programming language from scratch, and have gotten reasonably far. It reads just like Python, other than the fact that let is used ...
4
votes
0answers
126 views

Is there a standard name for this way of modifying graphs?

Let $G = (V, E)$ be an undirected graph. Let me take an edge $\{x, y\}$ (in blue in the drawing) such that $x$ and $y$ have other incident edges. Among the incident edges we choose one edge $e_x = \{...
3
votes
0answers
46 views

Complexity of #PP2DNF where we also count on the number of clauses

The #PP2DNF problem is the following: we have variables $X = \{x_1, \ldots, x_n\}$, $Y = \{y_1, \ldots, y_n\}$, and a positive partitioned 2-DNF formula, i.e., a Boolean formula of the form $\phi = \...
8
votes
0answers
94 views

Can we define a meaningful concept of exptime reductions (as opposed to polytime reductions) for classes like NEXP or NEEXP?

Typically we are only interested in polytime reductions as we are usually interested in showing a reduction from one NP-problem to another. However, if we consider larger complexity classes such as ...
1
vote
0answers
75 views

Complexity of planted root of a system of quadratic homogeneous polynomials?

Given homogeneous degree $2$ randomly chosen polynomials $f_1,\dots,f_{m}$ in $\mathbb Z[x_1,\dots,x_n,y_1,\dots,y_n]$ each with only monomials $x_iy_j$ with condition that the system $f_1=\dots=f_{m}=...
6
votes
1answer
230 views

What is the hardest instance for the group isomorphism problem?

Two groups $(G,\cdot)$ and $(H, \times)$ are said to be isomorphic iff there exists a homomorphism from $G$ to $H$ which is bijective. The group isomorphism problem is as follows: given two groups, ...
1
vote
0answers
34 views

Problems rephrased as quadratic unconstrained binary optimization

I was impressed when i came across Quadratic unconstrained binary optimization (QUBO) recently, and saw how one can rephrase many combinatorial problems into questions about optima of binary functions....
0
votes
1answer
114 views

First-order multi arity functions in dependent type?

(cross posted from Reddit https://www.reddit.com/r/dependent_types/comments/b1ts8b/firstorder_multi_arity_functions_in_dependent_type/? Take Agda for example, functions of multi arity is "encoded" as ...
2
votes
0answers
50 views

Inexpressibility of Second order

In finite model theory, Ehrenfeucht-Fraïssé games gives us tools to prove inexpressibility results for FOL. Pebble games do the same for infinitary logic with finitely many variables. Do we have such ...
5
votes
0answers
111 views

An axiom for John Major's Equality

In the the standard library of Coq, there is the axiom: Axiom JMeq_eq : forall (A:Type) (x y:A), JMeq x y -> x = y. Why isn't it provable? Can it be reduced ...
3
votes
1answer
119 views

How is SDP an extension of spectral algorithms?

In one of his lectures, Uri Feige described semidefinite programming (SDP) as ... an algorithmic technique that extends both linear programming and spectral algorithms. I know the basic ...
-3
votes
0answers
46 views

Why does Chaos Improve Evolutionary Algorithms?

I have presented an evolutionary algorithm using chaos theory (chaotic numbers) to solve an optimization problem. The results of the experiments show that this algorithm is much better than the same ...
-1
votes
0answers
8 views

Fastest way to read large wav files (or any large file) to python [migrated]

So i'm working on a school project where i have to work with large wav files ( > 250Mgb), and i wonder, why when i read such a file to audacity software, it take about 40 sec to be read and ploted, ...
3
votes
1answer
128 views

Intuitive explanation behind Goemans-Williamson randomized rounding

A very simple randomized cut algorithm achieves $1/2$ of the optimal value: just choose each vertex to be in the cut with probability $1/2$, independently. Goemans-Williamson does something more ...
3
votes
1answer
114 views

Compressing grammars by introducing ambiguity and left-recursion

This is a reference request. What is known about the following questions? Problem: Given a grammar $G$ (for example context-free) with language $L$ we can introduce a new grammar $G'$ which also ...
3
votes
0answers
58 views

Are there experiments in artificial life on the emergence of sexual reproduction (analogues)?

I'm aware of quite a few experiments on the emergence of replicators in various artificial life areas, e.g. from cellular automata to computer programs. Have any similar result been obtained on the ...
1
vote
0answers
54 views

Confusion about the visibility and arbitration relations in a formal framework for distributed consistency models

In the POPL'14 paper "Replicated Data Types: Specification, Verification, Optimality" and the book "Principles of Eventual Consistency", the authors propose a formal framework for specifying ...
1
vote
1answer
73 views

The SQ argument in Balazs Szorenyi's paper

I am asking about the proof in Theorem 5 (page 6) of this paper, http://www.inf.u-szeged.hu/~szorenyi/Cikkek/sq_d0_ext.pdf Quite a few things about this short argument seem unclear to me, Towards ...
0
votes
1answer
50 views

Counting sum of parities of cycle covers in cubic, planar, bipartite graphs

Let $G$ be a cubic (i.e. every degree exactly three), planar, bipartite graph. By Hall's theorem its edges can be partitioned into three perfect matchings. Take any such partition $M_0,M_1,M_2$ and ...
4
votes
0answers
79 views

Is there a universal gate set for classical probabilistic computing?

We know that NAND gates are universal for deterministic classical circuits, Toffoli gates are universal for reversible deterministic classical circuits, and Clifford+T is universal for quantum ...
2
votes
1answer
103 views

Optimal bounds for $k$-wise non-uniform random bits

Let $k\geq 2$ be a constant (in my case, $k=4$), and $n,t \geq 0$ be integers such that $2^t \leq n$. What is the smallest sample space (or, equivalent, how many true independent random bits are ...
3
votes
0answers
137 views

Take a NEXP-complete problem and then have the input in unary. Why is this not NP-complete?

It is known that if any unary language is NP-complete, then P=NP. Suppose we take a NEXP-complete language with input $x$ in binary and witness $y\in\{0,1\}^{2^{poly(|x|)}}$ such that the verifying ...
8
votes
0answers
200 views

Subset sum problem with at most one solution for any target

This question was originally asked on CS.se. A little bit of initial discussion can be found in the comments there. We first consider the search version of the subset sum problem: Given a set $S$ of ...
4
votes
0answers
136 views

Why is the Toffoli Gate named after Toffoli?

I was reading the following paper: Rolf Landauer, Irreversibility and Heat Generation in the Computing Process, IBM Journal of Research and Development, Volume 5, Issue 3, July 1961. On page 4, ...
11
votes
0answers
174 views

Computational Complexity of the Frobenius Problem

The Frobenius problem takes as input $n$ positive integers $a_1,\ldots,a_n$ with $\gcd(a_1,\ldots,a_n)=1$ and asks for the largest integer $F$ that cannot be written in the form $F=a_1x_1+a_2x_2+\...

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