All Questions

1
vote
1answer
63 views

Uniqueness of the distribution maximizing the channel capacity

Setting: We look at a discrete memoryless channel which takes an input probability distribution acting over symbols in $\mathcal{X}$ to an output probability distribution over symbols in $\mathcal{Y}$....
3
votes
2answers
144 views

Is counting simple cycles in $P$ for graphs of bounded tree width?

Motivation: Determining if a graph has a Hamiltonian cycle is $NP$-hard in general. However, determining if there is a Hamiltonian cycle is in polynomial time on graphs of bounded tree width, either ...
1
vote
0answers
28 views

Scheduling with Separation Constraint

There are $N$ types of jobs. For each $i$, we have to schedule $T/D_i$ jobs of type $i$ in $T$ timeslots. We know that $\sum_{i=1}^N 1/(D_i+1) = 1$. For each type $i$, the distance between two ...
7
votes
2answers
179 views

Determining how n-tuples are sorted as you search them?

I have a sorted list of $N$ n-tuples, but I do not know exactly how they were sorted. The person who sorted them did so by lexicographically ordering some permutation least-to-greatest. For example, ...
-1
votes
1answer
50 views

How is additive error handled in this simple algorithm? 'Product of all elements'

Say we have two unit vectors $\hat{u}, \hat{v} \in \mathbb{R}^n$ where $\hat{u} = (u_1,...,u_n)$ and $\hat{v}$ approximates $\hat{u}$. $~\hat{v} = (u_1+\epsilon, ...,u_n+\epsilon)$ where $\epsilon = \...
-1
votes
1answer
80 views

Why is $BPP^{NP}$ in polynomial hierarchy? [closed]

Why is $BPP^{NP}$ in the polynomial hierarchy? I know that $BPP$ is contained in $NP^{NP}$, so $BPP$ is inside $PH$. However, how does that imply $BPP^{NP}$ is inside the polynomial hierarchy?
2
votes
1answer
88 views

Biased binary search?

Suppose I have some pre-existing knowledge of where within a sorted array the element I am looking for lies, in the form of a probability distribution $P(i)$ that tells me the probability of the goal ...
2
votes
1answer
65 views

Hardness of LWE on not-uniform vector samples

The "usual decisional LWE": The challenger and the adversary get a common random matrix $A \in F_{q}^{m \times n}$. The challenger chooses a secret $s \in F_{q}^{n}$ and generates random (small) ...
7
votes
1answer
115 views

Reference request: Shortest homotopic curve via vertex releases

Let $C$ be a piecewise-linear path (or closed curve) in the plane, in the presence of polygonal obstacles. We would like to find the shortest path (or curve) homotopic to $C$. (A path $D$ is homotopic ...
2
votes
1answer
112 views

How to use a 𝑝-coin so a TM can decide an undecidable language in polynomial time? [closed]

In "Computational complexity- A modern approach" book (page 117) for the lemma 7.12 (following) the author mentioned that if the ρ is efficiently computable ρ-coin cannot give probabilistic algorithm ...
9
votes
2answers
286 views

Can three stacks be implemented in one array, with O(1) push/pop time?

Two stacks can be efficiently implemented using one fixed sized array: stack #1 starts from the left end and grows to the right, and stack #2 starts from the right end and grows to the left. Is the ...
2
votes
1answer
60 views

In external memory, is grouping equal elements easier than sorting?

Sorting an array will put equal elements adjacent to each other. So, in no model of computation can grouping equal elements be harder than sorting. In the RAM model, grouping equal elements is $O(n)$ ...
6
votes
2answers
136 views

Termination checking for Scott-encodings in System F with positive-recursive types

Is there any research on termination analysis on Scott-encodings in System F with positive-recursive types. All papers I have found use languages with constructors and case analysis (for example ...
10
votes
1answer
285 views

How hard is deciding the existence of Red-Blue perfect matching?

Two-colorable perfect matching problem is to decide whether a graph has coloring with two colors such that each node has exactly one neighbor the same color as itself. The problem was proven to be NP-...
1
vote
0answers
45 views

Asymptotic time required to simulate a Turing machine M for k steps

Problem: Given an encoding of a Turing machine M and a natural number k as input, find the output of M (given a blank tape) after k steps. Wikipedia's page on EXPTIME-complete says it takes O(k) time ...
10
votes
1answer
349 views

An obstruction like ETH

We know under $ETH$ we cannot solve $K$-SUM in $f(K)poly(nK)$ time under any function $f(K)$ (usually $2^{O(K)}$). Is there any conjecture that prevents a $(\log n)^{O(K)}$ complexity (this is ...
2
votes
0answers
112 views

A complexity-class of problems that cannot be solved in finite time

Consider the following game: Alice chooses a real function number $x\in [0,1]$; Bob has to guess the number by asking Alice any number of queries of the form "is $x > a$?" [where Bob can choose ...
-3
votes
1answer
95 views

Finding the maximum no. of people who get along in a group [closed]

Suppose that there are 15 people in a room. Assume that each person gets along with other people in the room (but not everyone). (Note that the "feeling is mutual" between any two people who are ...
0
votes
0answers
114 views

Where does a C-like language without heaps belong in the automata hierarchy?

Assume that the language C', unlike C, has well-defined semantics, but has similar features: pointers and manual memory management through malloc and free. Assume that C'' is the same as C' without ...
11
votes
1answer
540 views

Technical issue with PCP theorem proof

I am reading the proof from here and I stumbled upon a technical (yet crucial) problem. I know this is rather specific and the context is problematic, but I couldn't figure it out myself. In pages 51 ...
2
votes
0answers
94 views

Notion of “quotient” or “inverse” for recognizable tree languages?

Related to my previous question but this time I have a better idea of what I'm actually asking. I'm looking at the following operation on recognizable tree languages (i.e. regular tree grammars, ...
3
votes
1answer
87 views

Infinite $\beta \eta$-reduction sequence implies infinite $\beta$-reduction sequence

In Sorensen and Urzyczyn's book there is a lemma (1.3.11) which I am having a hard time proving. 1.3.11 Lemma: If there is an infinite $\beta \eta$-reduction sequence starting with a term $M$ ...
4
votes
0answers
60 views

What degree of hash function independence is needed for Bloom filters?

In the traditional analysis of Bloom filters, it's assumed that the hash functions are truly random functions, meaning that each hash function distributes each key uniformly and independently of each ...
2
votes
0answers
48 views

Regular Tree Languages are closed under quotient?

The Wikipedia page for Regular Tree Grammars notes that if $L_1$ and $L_2$ are regular tree languages, than $L_1 \setminus L_2$ is as well. However, it doesn't define this quotient operation for trees,...
6
votes
1answer
207 views

Uniform mortality problem for Turing Machines

Consider the following generalisation of the mortality problem for Turing Machines. Given a Turing Machine $M$. Is there a bound $k_M$ such that starting from any configuration $c$ machine $M$ ...
4
votes
1answer
143 views

What was the significance of Leslie Valiant's, “A Theory of the Learnable?”

It seems like two of the main takeaways were that there is a natural limit to what computers can learn, and learning is bounded by polynomial algorithms. Why was his paper significant in the broader ...
2
votes
1answer
74 views

Longest stack-sortable subsequence

Given an array of $n$ pairwise-different positive integers, the problem is to find the longest subsequence that is stack-sortable, i.e. avoiding the permutation pattern $231$. How fast can this ...
17
votes
1answer
251 views

Is the Set of all Primitive Words a Prime Language?

A word $w$ is called primitive, if there is no word $v$ and $k > 1$ so that $w = v^k$. The set $Q$ of all primitive words over an alphabet $\Sigma$ is a well known language. WLOG we can choose $\...
11
votes
0answers
153 views

$\exists \mathbb R$ and IP

We know NP$\subseteq$ $\exists \mathbb R$$\subseteq$ PSPACE=IP, but is there some more direct proof for $\exists \mathbb R\subseteq$ IP? What about the other direction, are there some Arthur-Merlin ...
8
votes
1answer
189 views

Turing Machines as Coalgebras

I'm looking to write a survey on the method of representing the dynamics of state-based computation within the framework of coalgebras. So far I've managed to find papers on coalgebra representations ...
0
votes
0answers
28 views

Alternating Delivery Problem

What is known about the complexity of the following problem: Suppose we have a complete bipartite graph $G(V,E)$ with disjoint sets $C$ and $T$. The candidate vertices, and the target vertices ...
1
vote
1answer
88 views

Vehicle scheduling

Suppose there are $n$ resources which can do some work. Each resource has a number of time windows: $tw_{i,k}=\{start_{i, k},stop_{i, k}\}$, such that the resource can perform its functions only ...
1
vote
0answers
72 views

Minimum cut with nonlinear objective function

Let $G$ be an undirected graph. The classic minimum (cardinality) cut problem asks for a cut $C\subseteq E(G)$, such that $|C|$ is minimum. Let us generalize it the following way: let $f$ be a ...
6
votes
1answer
149 views

Is there a relation between BBH (black box hypothesis) and SETH (strong exponential time hypothesis)?

Is there a relation between BBH (black box hypothesis) and SETH (strong exponential time hypothesis)?
0
votes
0answers
53 views

Which research fields deal with this variant definition of Boolean circuit depth?

Disclaimer: I admit that the question is not very clear. I think it cannot be helped because the question is very open-ended. First of all, I present the interested type of circuits. We only consider ...
0
votes
1answer
77 views

Densest k subgraph problem for outerplanar graphs?

The densest k subgraph problem aims to find a subgraph $H$ of a graph $G$ with exactly $k$ vertices that maximizes the number of edges $|E(H)|$. Does anyone know if there exists a polynomial-time ...
-1
votes
2answers
69 views

Machine Learning Algorithm To Fill Data Holes

I'm having trouble finding a good place to begin with this. I'm just looking for a name or point to start researching a Let's say I have 1000 records. 10 of these records are only 90% complete. The ...
3
votes
0answers
82 views

Counting quotient graphs, but not exactly

All graphs considered will be directed graphs $G=(V,E)$, with $E \subseteq V \times V$ (so possibly with self-loops). For $k \in \mathbb{N}_{\geq 1}$, I will write $[k]$ the set $\{1,\ldots,k\}$. A $k$...
1
vote
0answers
76 views

Is Combinatory Logic (CL) still relevant for programming language theory?

I've been reading up on R. Smullyan's "To Mock a Mockingbird" and Hindley's "Lambda-Calculus and Combinators: An Introduction". I've even read Schonfinkel's 1924 paper introducing the idea of ...
5
votes
1answer
151 views

Is there a notion of “inevitable reduction?”

I was just working on a semantics paper and realized I needed a notion of inevitable reduction. I came up with this definition: Let $\rightarrow$ be a binary relation. We say that $a$ inevitably ...
2
votes
0answers
66 views

References on generalization bounds

I'm looking for references (books, papers, lecture notes etc) on generalization bounds and their proofs. Specifically, I'm looking to fully understand the technique of defining a hypothesis class (or ...
7
votes
0answers
133 views

NP-hardness proof of selecting the ''fittest'' topological sequence of a DAG

Given a directed acyclic graph (DAG) with $n$ vertexes $V=\{v_1, v_2,...,v_n\}$ and a given permutation of those $n$ vertexes $P=[p_1, p_2,..., p_n]$ that $\forall i, p_i\in V$. Note that $P$ could ...
9
votes
1answer
506 views

What is the “question” that programming language theory is trying to answer?

I've been interested in various topics like Combinatory Logic, Lambda Calculus, Functional Programming for a while and have been studying them. However, unlike the "Theory of Computation" which ...
0
votes
0answers
21 views

Does optimal fitting flat must pass through the mean of the point set?

I am confused about a statement made in the paper Linear Time Algorithm for Projective Clustering, section 5.1, second paragraph, second line. Project clustering is a natural generalization of k-...
0
votes
1answer
79 views

Are both safety and liveness properties closed under finite intersection?

Given two safety properties $P_1$ and $P_2$, is their intersection $P_1 \cap P_2$ also a safety property? Similarly, if $P_1$ and $P_2$ are liveness properties, is $P_1 \cap P_2$ also a liveness ...
3
votes
0answers
165 views

In light of Raz and Tal's results, what can we say about whether there's a BQP problem for each level of the polynomial hierarchy?

[cross-posted on QCSE a couple of weeks ago] Every Venn diagram or Hasse diagram I see illustrating the "standard model" of computational complexity describes a universe of $\mathsf{PSPACE}$ problems,...
3
votes
0answers
92 views

What can be some bachelor thesis ideas in Quantum random walks?

Note: Cross-posted on Quantum Computing Stack Exchange. I am an undergraduate, reading about quantum information and quantum technology. For about some time, I have been interested in the ...
3
votes
1answer
159 views

String theory based computations

I was reading Arora and Barak's book on computational complexity and in the section on 'criticism on Turing machine model and the class P' along with quantum computer it also mentions possibilities of ...
13
votes
1answer
428 views

Can one efficiently uniformly sample a neighbor of a vertex in the graph of a polytope?

I have a polytope $P$ defined by $\{ x : Ax \leq b, x \geq 0\}$ . Question: Given a vertex $v$ of $P$, is there a polynomial time algorithm to uniformly sample from the neighbors of $v$ in the graph ...
32
votes
4answers
4k views

Single author papers against my advisor's will?

I am a third year PhD student in an area of theoretical CS that would like advice for a difficult situation with my advisor. My advisor is not involved in my research projects at all. In particular, ...

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