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-2
votes
0answers
17 views

What is the analog of PPAD and TFNP for Logspace?

What are the analogs of PPAD and TFNP for logspace? Is any of these known to be in $FL$?
-1
votes
0answers
12 views

polynomial over a field

Example: P = a(xy) + b(x^2y) + c(yz^3) + .... when speaking of a "polynomial over a field F" does one mean that the coefficients (a, b, c,...) are drawn from the field F, or the variables (x,...
0
votes
0answers
15 views

k-Median Problem With Restricted Centers

The $k$-median problem is defined as follows: Given a set $C$ of clients and a set $L$ of facility locations defined over a distance metric $d$. Open a set $F$ of $k$ facility in $L$ such that the ...
1
vote
1answer
26 views

star height of star-free languages

I'm interested in the (restricted) star-height of star free-languages. Recalling the definitions: the star height $h(\mathtt{e})$ of a regular expression $\mathtt{e}$ is $0$ if $\mathtt{e}= \...
-2
votes
0answers
27 views

schwartz-Zippel identity testing

I apologize for the naive question: according to Schwartz-Zippel, the probability of obtaining a root of a polynomial over the field F, of degree d, is d/|F|. So, if the coefficients of the polynomial ...
-3
votes
0answers
24 views

Permutation Graphs is Chordal?

Whether the permutation graphs are a subclass of the chordal graphs? If not, what is the counter-example?
6
votes
0answers
82 views

Complexity of NFA to DFA minimization with binary threshold

What is the complexity of the following problem? Given an NFA $A$ and a number $k\in \mathbb{N}$ in binary encoding, does there exist a DFA $B$ with at most $k$ states such that $L(A)=L(B)$? ...
-1
votes
0answers
74 views

Any problems for which we know the complexity, but no algorithms with the same time?

I suddenly found myself wondering if there are any problems for which the complexity (time or space or anything else) is proven, say to be O(n^2), but for which the best known algorithms are worse ...
-3
votes
0answers
31 views

Asymptotic Analysis of code that are unusual [closed]

We all know that the RUN Time of most of our program are Big O of linear time, quadratic time, cubic time or log time. But Can this be in unusual or uncommon poly time like $x^6-y$ or cosine function ...
2
votes
0answers
73 views

Lower bound for the OR problem

Let us have booleans $x_1, \cdots, x_n$. Any algorithm that determines $\bigvee_1^n x_i$ with probability at least $2/3$ requires $\Omega(n)$ time. It is not too difficult to prove this, but the proof ...
-2
votes
0answers
60 views

Example of any non-NP decision problem without invoking time-hierarchy theorem

References appreciated for any problem decided by a Turing machine with a finite transition table that does not belong to the class NP. The non-membership is proven without the use of diagonalization ...
1
vote
1answer
84 views

Are there an algorithm that find Minimum spanning tree in $O(n^2\log\log^*n)$?

Given completed metric weighted graph $G=(V,E)$ that have $n$ vertices. Are there an algorithm that find MST of $G$ in $O(n^2)$? I read abstract of this paper that mentioned an algorithm with running ...
2
votes
0answers
54 views

Does a graph resulting from the union of triangles has a particular name?

I have different simple triangle graphs. As an instance, $G_1=(V_1,E_1)=(\{1,2,3\},\{\{1,2\},\{2,3\},\{3,1\}\})$ and $G_2=(V_2,E_2)=(\{1,4,5\},\{\{1,4\},\{4,5\},\{5,1\}\})$. The union of both graphs ...
-2
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0answers
17 views

algebraic specification online course, do you know any?

I am in need of an online course/tutorial on algebraic specification. Do you know any good resource with problems with solutions?
2
votes
1answer
86 views

exact path cover for undirected graph

In a Python plotting application, I have an undirected connected graph, not necessarily simple, that I'd like to cover with paths such that each edge is contained in exactly one path. The number of ...
-1
votes
1answer
89 views

Derandomizing arbitrary width *read-many* and *ordered* branching programs?

Modifying following TedP We know that derandomizing width $5\leq k\in O(1)$ read many branching programs is equivalent to $BPNC^1=NC^1$ and derandomizing width $k\in\Omega(n)$ read once ordered ...
-8
votes
0answers
56 views

Does this sequence of quantified boolean formulas make sense to anyone else? most of these qbfs are valid

do all logicians on earth know that a question is a qbf? yes and they know the answer to a qbf is always yes or no? yes ok good all logicians know that solving one qbf is hard and buggy? yes but ...
2
votes
1answer
74 views

Regular Expressions that converts into unambiguous automata

Brüggemann-Klein and Wood (1992) proved that a certain kind of regular expressions, that they call “Deterministic Regular expressions”, when converted into automata using the Glushkov's Construction, ...
5
votes
0answers
65 views

Fine-Grained Hardness for Undirected Hamiltonicity

The fastest known algorithm for detecting Hamiltonian cycles in directed graphs on $n$ nodes runs in essentially $2^n\text{poly}(n)$ time. However, for undirected graphs on $n$ nodes, there is an ...
1
vote
0answers
67 views
+100

Fastest Known Algorithm for $k$-Dimensional Matching and $k$-Exact Cover

Given a $k$-uniform hypergraph $G$ (i.e., each edge of $G$ contains precisely $k$ vertices) on $n$ vertices, the $k$-Exact Cover problem is the task of deciding if there exists $n/k$ edges in $G$ ...
0
votes
0answers
28 views

Bounded-Frequency Minimum Set Cover Problem

Consider the special case of the minimum set cover problem where each element of the universe occurs in at most 3 sets. Can this problem be solved in polynomial time? Is there a nontrivial upper ...
1
vote
0answers
94 views

Does any physical process constitute a "computation"? [closed]

I am trying to sharpen the convex hull of what seems like a (surprisingly) stubborn concept to enclose based on answers here, as well as conversations with others, around the nature of what actually ...
1
vote
0answers
50 views

Canonical tester for dense graphs: from tester to removal lemma?

A theorem of Goldreich and Trevisan [1] on property testing in the dense graph model states the following (docusing on the one-sided part): Suppose there exists a one-sided testing graph algorithm ...
1
vote
1answer
51 views

Maximize the absolute value of connected nodes after $k$ modifications

Given a graph $G=\{V,E\}$, each node $i$ has a value $v_i$. Given budget $k$, we have $k$ chance to add 1 or minus 1 for a node's value, for example, $v'_i=v_i+1$ or $v'_i=v_i-1$. In particular, $v'_i$...
2
votes
0answers
73 views

On-line pagerank in a streaming DAG (Directed Acyclic Graph)

Assume a DAG (Directed Acyclic Graph) is given as a stream of edges such that edge $(u,v)$ is given only after all incoming edges of $u$ are given. Let us denote by $n$ and $m$ the number of vertices ...
7
votes
2answers
127 views

Algebraic characterisation of star-free safety languages

It is known that star-free languages are definable by aperiodic syntactic monoids. But is there any algebraic characterisation of star-free safety $\omega$-languages? Edit: A language $L$ is safety if ...
-1
votes
1answer
71 views

Non-(PAC)-Learnable Classes

I'm learning about PAC-learnability. I've figured out how to show that a class of classifiers is PAC-learnable, but what about if I want to show that a class of classifiers is not PAC-learnable? How ...
1
vote
1answer
109 views

Divide and Conquer Algorithm for 1-Median Problem

Let $P_1$ and $P_2$ be two disjoint point sets in $\mathbb{R}^d$ and $n = \vert P_1\vert = \vert P_2\vert$ and $P = P_1\cup P_2$. Let $c^\star$ be the optimal 1-median for $P$ and $opt^\star$ is the ...
-2
votes
0answers
60 views

Approximating the number of triangles using $\ell_0$ sampling

(Previously posted to cs.SE but with no luck. Apologies if the questions is too basic.) How do you solve the following question, from this assignment? Question 2. Consider a stream that consists of ...
1
vote
1answer
151 views

State of the art approximation algorithm for $\text{MAXCUT}$ that does better than Goemans and Williamson

I had thought that the Goemans-Williamson approximation algorithm was the best for MAXCUT. To quote from Wikipedia: The polynomial-time approximation algorithm for Max-Cut with the best known ...
0
votes
0answers
48 views

Minimal lexicographical path on DAG in O(||V| + |E|)

Let's assume, that we have directed asyclic graph and nodes U and V. Every edge of this graph is marked with alphabet letter (alphabet size is fixed). Is there any way to answer, what is the shortest ...
6
votes
1answer
250 views

Cook inspiration for NP completeness

An academic descendant of Cook just lectured on NP completeness. He said that the idea came from a well-known theorem in first-order logic that talks about completeness of satisfiability for ...
3
votes
1answer
66 views

Encapsulation of OOP and referential transparency of functional programming

I would like to understand more about the 'orthogonality' of OOP and functional programming. What makes me confused is the 'encapsulation' of OOP and 'referential transparency of functional ...
5
votes
0answers
108 views

Halting problem for finitary PCF

Is the halting problem decidable for finitary PCF? By "halting problem" I mean the problem of deciding whether a closed PCF term evaluates to bottom under the denotational semantics of PCF. ...
-2
votes
0answers
52 views

Show a class of hypothesis is not PAC-learning (realizable)

I'm currently studying PAC learning (realizable). I think for me, it is easy to show that a class of classifiers is PAC-learnable. However, I am not sure how to prove that a class of classifiers is ...
0
votes
0answers
48 views

Finding the best $k-$subset which maximizes a matrix sum

Let $M\in \mathbb{R}^{N\times N}$ be a given matrix and $k\ge 2$ be a given integer. Then my question is the following optimization problem: Is there a polynomial-time solution to the following ...
-1
votes
0answers
60 views

A Special case of Weighted Set Cover Problem

We are given a set P of k points in the plane, and a set S of simple polygons that are triangulated into a set T of triangles, each triangle t in s has a weight that is 1 if we choose no triangles (w(...
0
votes
0answers
69 views

Large CLIQUE approximation

I am interested in algorithms to identify large cliques in graphs where the largest clique is a large fraction (definitely greater than half, perhaps as great as 4/5) of the total number of vertices. ...
2
votes
1answer
72 views

Can this special case of Node Weighted Steiner Tree be solved in polynomial time?

Consider the node-weighted steiner problem: Input: a graph $G=(V,E)$, a set $T\subseteq V$ of terminals, a weight function $w: V\setminus T \to \mathbb{R}_+$. Output: a minimum weight subset $S \...
4
votes
1answer
172 views

Upper bound on the expected number of correct bits via a "lossy compression"

Consider the following "compression problem" for a pair $(C,D)$ of algorithms: $C$ receives a uniformly random $x \in \{0,1\}^n$ and outputs a smaller bit string $y \in \{0,1\}^s$. Algorithm ...
0
votes
0answers
108 views

Can this NP-hardness proof for Super Mario Brothers (and other games) be simplified?

In "Classic Nintendo Games are (Computationally) Hard", a generalized framework based on reducibility of 3-SAT for proving NP-hardness of classic Nintendo games is presented, and several ...
7
votes
0answers
108 views

Can exponential-size depth-2 $CC^0[m]$ circuits with generalized $MOD_m$ gates compute arbitrary functions from $Z/mZ$ to $Z/2Z$?

Terminology $CC^0[m]$ is the set of polynomial-sized, constant depth circuits consisting entirely of $MOD_m$ gates for some $m \geq 2$, where a $MOD_m$ gate outputs a 1 if and only if the sum of its ...
3
votes
0answers
81 views

Why is the ellipsoid method numerically unstable?

In the Ellipsoid method wikipedia entry under the performance section, it is mentioned that the Ellipsoid method often times is numerically unstable in practice: "On even "small"-sized ...
1
vote
1answer
81 views

Maximally Permissive Strategies for Safety Properties

Different definitions of maximally permissive strategies exist. For instance, in (Bernet, Janin, and Walukiewicz 2002), strategies are compared by looking at inclusion of the behaviors/outcomes they ...
0
votes
0answers
37 views

Is it possible to count the total number of local minima for a scalar, multivariate function?

We can assume the function is differentiable, but it is also non-convex and setting the gradient equal to zero has no analytical solution. We can also assume that the domain is bounded, namely the ...
1
vote
0answers
47 views

Decision tree vs. pebble game lower bounds

This question concerns two types of lower bounds. In a pebbling lower bound, we are concerned with the complexity of constructing the output from the input. For example, if the only way we could ...
3
votes
0answers
57 views

Exact FPT Algorithm for Continuous Euclidean $k$-Means

The continuous Euclidean $k$-means problem is defined as follows: Given a set $X$ of $n$ points in $d$ dimensional Euclidean space $\mathbb{R}^{d}$. Given a parameter $k>0$, find a partitioning $P$ ...
0
votes
0answers
20 views

Fast algorithms for convex-convex quadratic fractional programming

What are the fastest algorithm(s) (possibly approximation algorithms) for solving convex-convex quadratic fractional programming problems, i.e. optimization problems of the form $$ \begin{align*} \sup&...
2
votes
2answers
102 views

Status of certain problems in knot theory

I found it somewhat difficult to understand the status of certain problems from knot theory. Is it correct to say that it's been neither proved nor disproved that any of the following problems are NP-...
5
votes
0answers
124 views

$\mathbf{AC}^0$ lower bounds for $\mathsf{Gap}\text{-}\mathsf{Max3SAT}$

Various gapped maximization problems are known not to be $\mathbf{NP}$-hard under $\mathbf{AC}^0$ reductions, e.g., $\mathsf{Gap}_{1,\epsilon}\text{-}\mathsf{Max3SAT}$ (see, e.g., Proposition 4 of ...

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