All Questions

Filter by
Sorted by
Tagged with
0
votes
1answer
89 views

Is Hamiltonian cycle fixed parameter tractable with parameter clique cover?

We conjecture that Hamiltonian cycle is fixed parameter tractable with parameter clique cover, given $k$-clique cover. Let $G$ be connected simple graph. $k$-clique cover of graph $G$ is partition ...
2
votes
1answer
63 views

Does distance-2 coloring fit in Telle and Proskurowski 's algorithm for partial-k trees?

(This question is inteneded for people who have heard of "Vertex Partitioning Problems" framework of Telle and Proskurowski. Others may dig in only if they are interested in practical algorithms for ...
0
votes
1answer
91 views

Is the counting version of 1-in-3 Sat #P-complete?

In the paper "Hard Tiling Problems with Simple Tiles", Moore and Robson prove that Cubic Planar Positive 1-in-3 Sat in NP-complete by a reduction from Positive 1-in-3 Sat. Cubic Planar Positive 1-in-...
5
votes
1answer
122 views

Known property? Maximum radius of connected induced subgraph

I was wondering if the following graph property has a name and has been researched: Consider any connected induced subgraph $H \subseteq G$. Then $r(G)$ denotes the maximum radius of any such $H$. I ...
6
votes
1answer
86 views

Determining if a word of specific length exists that is not accepted by a NFA

It is known that the problem of determining if an NFA accepts every word is PSPACE-COMPLETE, meaning it is also NP-Hard, but is this weaker version of the problem still NP-hard? Given an NFA and a ...
0
votes
0answers
46 views

Randomized Reduction for Maximization Problem

I have two maximization problems $P_1$ and $P_2$ where the decision version $L_1 = \{(x, t) : \operatorname{Val}_1(x)\ge t\}$ of $P_1$ is $\mathsf{NP}$-complete. Let $f:P_1\to P_2$ be a randomized ...
0
votes
0answers
83 views

NP-Hard Knapsack Instances

Consider the classic Knapsack optimization problem (KP): Given $p_1, \dots, p_n, w_1, \dots, w_n, B\in\mathbb N$, compute a solution $I\subseteq \{1,\dots,n\}$, such that $\sum_{i\in I} w_i \leq B$ ...
28
votes
4answers
1k views

Is there a result in computability theory that does not relativize?

I was reading Andrej Bauer's paper First Steps in Synthetic Computability Theory. In the conclusion he notes that Our axiomatization has its limit: it cannot prove any results in computability ...
-3
votes
1answer
92 views

Is this a good definition of computability? [closed]

I still haven't found a good definition of computability. All the definitions are either too vague, or they delegate the definition to another loaded term like "anything that uses math to solve a ...
2
votes
0answers
184 views

Fast algorithms for evaluating functions with high Kolmogorov complexity

Motivation: I am motivated by a concrete example that occurs in neuroscience, dendritic computation, which may be approximated by functions computable on binary trees [1]. To be more precise, I ...
2
votes
0answers
100 views

Equational Theories for Type Systems

I was reading through Gunter's Semantics of Programming Languages: Structure and Techniques and in the second chapter on simply typed $\lambda$ calculus he introduces an equational theory with $\beta\...
-2
votes
1answer
135 views

Minimum vertex cover and odd cycles

Suppose we have a graph G without odd cycles. Consider the minimum vertex cover problem of G formulated as a linear programming problem, that is for each vertex $v_{i}$ we have the variable $x_{i}$, ...
2
votes
1answer
249 views

Can recursion be replaced with a finite set of higher-order functions? [closed]

I am wondering if there is some proof that all recursive algorithms can be rewritten to use some known set of higher-order functions instead of recursion. I'm talking about functions like fold, map, ...
13
votes
5answers
13k views

Why can machine learning not recognize prime numbers?

Say we have a vector representation of any integer of magnitude n, V_n This vector is the input to a machine learning algorithm. First question : For what type of representations is it possible to ...
24
votes
5answers
3k views

Implications of unprovability of $P\neq NP$

I was reading "Is P Versus NP Formally Independent?" but I got puzzled. It is widely believed in complexity theory that $\mathsf{P} \neq \mathsf{NP}$. My question is about what if this is not ...
15
votes
2answers
748 views

Büchi automata with acceptance strategy

The problem Let $A=\langle \Sigma, Q, q_0,F,\Delta\rangle$ be a Büchi automaton, recognizing a language $L\subseteq\Sigma^\omega$. We assume that $A$ has an acceptance strategy in the following sense ...
4
votes
1answer
949 views

Is an algorithm with an approximation factor of 4000 useful?

A paper published in SODA this year (2019) proposed a constant approximation algorithm for the lower bounded facility location problem with general lower bounds. To my surprise, when reading the ...
2
votes
1answer
90 views

How to choose good diagonals when partitioning an orthogonal polygon into rectangles?

Following this answer on MathOverflow and section 3 of the linked paper by David Eppstein on how to split an orthogonal polygon into rectangles I came to a point where I just fail to understand how to ...
0
votes
1answer
180 views

Does two-sided error have more capability than one-sided error?

From $P=RP$ extrapolation we might think $EXP=REXP$. What evidence do we have $BPP\subseteq REXP$? What consequence $REXP\subseteq BPP$ gives other than what $EXP\subseteq BPP$ gives?
1
vote
1answer
166 views

Example of a $U^\omega$ that is not Deterministic Büchi recognizable

Is there a regular language $U$, for which $U^\omega$ is not a Deterministic Büchi recognizable language. I have been thinking over it for some time, but have been unable to come up with an example.
3
votes
1answer
122 views

Intersection of two deterministic parity automata

Given two deterministic parity automata $A_1=(Q_1,\Sigma,\delta,q_{01},c_1)$ and $A_2=(Q_2,\Sigma,\delta,q_{02},c_2)$ with the finite set of states $Q_i$, the finite alphabet $\Sigma_i$, the ...
0
votes
0answers
58 views

What is Undefined Behaviour mapped to with Curry-Howard Correspondence?

As far as I understand, Curry-Howard Correspondence is metaphorically a magical mirror which makes programming concepts and tricks be seen as mathematical theorem/proof elements and vice versa. ...
1
vote
1answer
128 views

Kolmogorov Complexity of the composition of two computable functions

Let's suppose we encode two computable functions $f$ and $g$ as binary strings so $f,g \in \{0,1\}^*$. What I am curious about is whether we can find good upper and lower bounds for: \begin{equation}...
3
votes
1answer
138 views

Convex polygons inclusion relation

I have the following problem which came as a subproblem in some work I was doing and I am completely stuck. Note that I am interested in it only in terms of worst case time complexity (not heuristics ...
-1
votes
1answer
58 views

Generating set of a group and relation to diameter?

Is there an efficient algorithm to test if a given subset of symmetric group generates the symmetric group? Drawing the Cayley graph and testing for all pairs reachability is one way however that ...
14
votes
3answers
2k views

White elephant gift exchanges: mechanisms for fair division

A popular game at holiday parties in North America is the white elephant gift exchange. In brief (ignoring variations) it works as follows: There are $n$ people and $n$ wrapped gifts. Players are ...
2
votes
0answers
87 views

What is the difference between ${\bf P ^{\bf FewP}}$ and ${\bf UP ^{\bf FewP}}$?

What is the difference between ${\bf P ^{\bf FewP}}$ and ${\bf UP ^{\bf FewP}}$ ? In other words, what is the language that can be decided by ${\bf UP ^{\bf FewP}}$, but cannot be decided by ${\bf P ^{...
2
votes
0answers
89 views

How fast can we perform DFT on a Log-RAM computer?

The question is how fast we can perform an $n$ coefficient discrete Fourier transform on the log-RAM model of computation. If we assume that we can do arithmetic operations on registers of size $\log{...
0
votes
2answers
143 views

Turing meta-oracle

Let H(P) be some program that given P('s source code) computes whether or not P terminates, i.e. solves the halting problem. H only needs to terminate if P terminates. (This disallows solutions like ...
1
vote
1answer
63 views

Data structures for embedded simplicial complexes

I am looking for a data structure to encode an $n$-dimensional simplicial complex with an embedding in $\mathbb{R}^{n+1}$. I am aware of combinatorial maps, which generalize rotation systems of planar ...
4
votes
1answer
230 views

Analogue of $k$-wise independence for other distributions than uniform

I am looking for the name of the following notion (in order to look it up for myself), and possibly pointers to the corresponding literature. Let $D$ be a fixed distribution over $\{0,1\}^n$, and $1\...
5
votes
1answer
190 views

Latest word on cross validation?

It's a standard result leave-one-out cross-validation is an unbiased estimator of the risk (see, e.g., Lemma 4.1 in Mohri, Rostamizadeh, Talwalkar). Are there any "better" results? Such as, say, with ...
18
votes
3answers
545 views

Examples of the value of proofs for algorithms

In teaching Intro. Algorithms to undergrads, one of the most difficult tasks is to motivate why they need to know how to prove things about algorithms. (For many students, at least in many US ...
0
votes
1answer
150 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 ...
5
votes
1answer
206 views

Applications of Barendregt–Geuvers–Klop conjecture

I was learning about type systems from Benjamin C. Pierce's Types and Programming Languages and came across the Lambda cube in the chapter on Higher-Order Polymorphism. After reading up more about it ...
3
votes
0answers
88 views

Isomorphic subforest problem

I recently read that the following problem is NP-Complete: Given a tree $T$, and a forest $F$, is there a subgraph of $T$ isomorphic to $F$? The reference provide was to the textbook “Computers and ...
7
votes
1answer
437 views

Indications that strengthen the conjecture: NEXP ⊊ EXP^NP

I am trying to find indications that strengthen the conjecture of NEXP ⊊ EXP^NP. Clearly NEXP ⊆ EXP^NP, and there are some hints that this inclusion is proper. Some Examples: 1. A paper by Shuichi ...
0
votes
0answers
30 views

What is the current state of the art with respect to First Order Bayesian Networks?

The below is a survey paper: https://ieeexplore.ieee.org/document/5579472 Is there any significant updates to this? They mention Bayesian Logic Programs (BLP), Bayesian Logic (BLOG) and Multi-Entity ...
3
votes
0answers
82 views

In quantum money schemes, how is the list of serial numbers provided?

Public key quantum currency generally includes $k$ pairs ($S_\psi,\vert \psi\rangle)$ of classical information (bits) $S_\psi$ and quantum information (qubits) $\vert \psi\rangle$. In many examples,...
3
votes
2answers
122 views

Understanding non-equivalence of proof lengths according to proof systems

Here, in section 4.3, Fortnow says: But to prove P != NP we would need to show that tautologies cannot have short proofs in an arbitrary proof system. I am ...
15
votes
3answers
1k views

Checking formulas with two quantifiers ($\forall \exists$) - 2QBF

SAT solvers give a powerful way to check the validity of a boolean formula with one quantifier. For instance, to check the validity of $\exists x . \varphi(x)$, we can use a SAT solver to determine ...
2
votes
1answer
207 views

Prime factorisation of decidable problems

Disclaimer: I am not a theoretical computer scientist. The set of decidable problems $\mathbb{D}$ is countable so $\lvert \mathbb{D} \rvert = \lvert \mathbb{N} \rvert$ and this led me to the ...
3
votes
0answers
50 views

Gradient descent step size for strongly convex functions

Suppose we are optimizing a strongly convex function $f(x)$ via gradient descent $x_{t+1} = x_t - \eta_t \nabla f(x_t)$. By strongly convex I mean that $f(x+h) \ge f(x) + \langle \nabla f(x), h \...
14
votes
2answers
1k views

NP-hard problems with very fast exponential-time algorithms

NP-hard problems with very fast exact exponential-time algorithms, say with $O(1.01^n)$ time, are very rare. Is any fact like "For any constant $\epsilon>0$ there is an NP-hard 'natural' ...
0
votes
0answers
56 views

Complexity of multi-objective optimization problems

How can we define and prove the worst-case complexity of multi-objective optimization problems (MOOP)? It is easy to see that, if one of the objectives is an NP-Hard optimization problem, then the ...
4
votes
1answer
803 views

Knapsack with dependent profits (pairs of items)

I'm working on a problem which MAY be reduced to the following version of Knapsack: Suppose two items $e_i$ and $e_j$ have profit $p_i$ and $p_j$ respectively. However, if both items are present in ...
7
votes
2answers
251 views

Maximum shortest word accepted by pushdown automata

Given a fixed alphabet, consider all deterministic pushdown automata with $n$ states that accept a nonempty language. What is the maximum length of the shortest word accepted by a deterministic ...
3
votes
1answer
86 views

Meet of integer partitions

An integer partition of $n$, $A$, is a multiset of positive integers such that $\sum_{a \in A} a= n$. We say that $B \leq A$, if there exists a map $\phi: |B| \to |A|$, such that for $a \in A$, we ...
2
votes
1answer
71 views

About estimating escape time of gradient Langevin dynamics

I am trying to understand the argument in the proof of Lemmma 6.3 (page 18) of this paper https://arxiv.org/abs/1902.08179. Let me summarize the conceptual crux of the argument here using a slightly ...
12
votes
1answer
865 views

Consequences of $\oplus \mathbf{P} \subseteq \mathbf{NP}$

I have part of a proof attempt of $\oplus \mathbf{P} \subseteq \mathbf{NP}$. The proof attempt consists of a Karp reduction from the $\oplus \mathbf{P}$-complete problem $\oplus$3-REGULAR VERTEX COVER ...

15 30 50 per page
1
3 4
5
6 7
212