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Questions tagged [reference-request]

Reference-request is used when the author needs to know about work related to the question.

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13
votes
1answer
511 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 ...
0
votes
0answers
40 views

Incompleteness and term extraction

Is there a formalization, which from a proof that a system includes enough arithmetic extracts an arithmetic sentence in the language of PA, which is not provable in the given system? Imagine the ...
13
votes
1answer
269 views

Why is the Greedy Conjecture so difficult?

I recently learned about the Greedy conjecture for the Shortest Superstring Problem. In this problem, we are given a set of strings $s_1,\dots, s_n$ and we want to find the shortest superstring $s$ ...
9
votes
1answer
117 views

The source of the modular decomposition graph

When introducing graph modular decomposition, most authors use the 11-vertex graph, which I copy from wikipedia. The question is who is (are) the original designer of it. (I'm not asking who drew ...
3
votes
0answers
73 views

Eliminating tautological axioms in tree-like $k$-DNF resolution

The propositional proof system $k$-DNF-resolution, a.k.a. $Res(k)$, is a generalization of propositional resolution, where the lines in a proof are $k$-DNF formulas, i.e., disjunctions of $k$-terms of ...
6
votes
1answer
305 views

On theoretical aproaches for solving $\mathsf{SAT}$ in special cases

In what cases $\mathsf{SAT}$ can be solved in polynomial time? I know two cases: $2$-$\mathsf{SAT}$ and Horn-$\mathsf{SAT}$. Question 1: Is there a reference with algorithms for solving $\mathsf{...
8
votes
0answers
122 views

A canonical complete problem for EXP and NEXP in terms of formulae

3SAT is a complete problem for NP. TQBF is a complete problem for PSPACE. Is there direct way to define canonical complete problems for EXP and NEXP in terms of boolean formulae? I have only seen ...
42
votes
22answers
4k views

What hierarchies and/or hierarchy theorems do you know?

I am currently writing a survey on hierarchy theorems on TCS. Searching for related papers I noticed that hierarchy is a fundamendal concept not only in TCS and mathematics, but in numerous sciences, ...
2
votes
2answers
132 views

What are some good resources for strengthening my theoretical foundation for machine learning?

I'm a computer science major and I'm taking a lot of machine learning courses. I'm finding that my theoretical foundation on subjects like calculus and linear algebra are not as strong as I'd like ...
7
votes
3answers
214 views

Can Non-termination be considered an algebraic effect?

Non-termination is sometimes considered an effect. I have been reading about algebraic effect systems (What is algebraic about algebraic effects and handlers?), and I suspect non-termination (like ...
4
votes
1answer
103 views

Satisfiability problems with restricted (not bounded) number of occurrences per variable

Intro It is known that SAT is hard even when restricted to, e.g., formulas with exactly 3 literals per clause and at most 4 occurrences per variable. On the other hand it is easy if there are exactly ...
4
votes
1answer
193 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\...
13
votes
2answers
685 views

Online Algorithms books

Are there any recent books on Online Algorithms? I know of only two books on the subject. Online Computation and Competitive Analysis by Allan Borodin and Ran El-Yaniv: This is a classic but old book,...
5
votes
1answer
143 views

Counting avoiding improper 3-colorings

Given a graph $G=(V,E)$, what I call an improper $3$-coloring of $G$ is simply a function $c:V \to \{1,2,3\}$. I say that $c$ is $1$-$2$-avoiding when there do not exist two adjacent nodes $u,v$ with $...
16
votes
2answers
726 views

Complexity of counting the number of edge covers of a graph

An edge cover is a subset of edges of a graph such that every vertex of the graph is adjacent to at least one edge of the cover. The following two papers say that counting edge covers is #P-complete: ...
5
votes
1answer
316 views

Where is the quote “Informal proofs are algorithms, formal proofs are code” from?

Does anyone know the origin of the quote, Informal proofs are algorithms; formal proofs are code. Its made in Benjamin C. Pierce et al.'s Software Foundations.
10
votes
2answers
467 views

Lattice problems

There has been a fair amount of work on computational problems for partial orders (e.g., recognition, jump number, comparability graph recognition, etc...). I am curious what work specific to ...
4
votes
1answer
165 views

Name for a special family of languages?

I was wondering whether there is a standard name in the literature for the following family $\mathcal{F}$ of languages over any finite alphabet $\Sigma = \{a_1,\ldots,a_k\}$: $\mathcal{F}$ consists ...
4
votes
0answers
116 views

Characterizing the ANF of Single-Cycle Boolean Permutations

Given a function $F: \{0, 1\}^n \to \{0, 1\}^n$, we say that $F$ is a boolean permutation (also sometimes called a vectorial boolean function or an s-box in the literature) if $F$ is a bijection. We ...
4
votes
2answers
321 views

A variant of #POSITIVE-2-DNF

Let $G=(V,E)$ be an undirected graph. I call a valuation of $G$ a function $\nu: V \to E$ that maps every node $x \in V$ to an edge incident to $x$ (so that there are $\prod_{x \in V} d(x)$ valuations ...
3
votes
0answers
107 views

Earliest forbidden subgraph characterisation

I wonder, what was the first non-trivial graph class for which there was a forbidden (induced) subgraph characterisation ? Of course, bipartite graph is one example but I am considering it as trivial ...
5
votes
1answer
223 views

The asymptotic behavior of a recurrence related to stable matchings

I would like to provide asymptotic estimates for a sequence defined (for n a power of 2) as follows: $$a_1 = 1, a_2 = 2$$ $$a_n = 3a_{n/2}^2 - 2a_{n/4}^4$$ Apparently, Knuth was able to prove that ...
2
votes
1answer
147 views

Possibility of hierarchy with $UP$ class?

I am not sure if this is a cheap query. However I am unable to find this myself. So I am posting here. The standard complexity class is built with $NP$ and $coNP$ and leads up to $PSPACE$. The ...
9
votes
2answers
301 views

Consequences of OWFs for Complexity

It it well-known that the existence of one-way functions is necessary and sufficient for much of cryptography (digital signatures, pseudorandom generators, private-key encryption, etc.). My question ...
9
votes
1answer
191 views

Proof for Upper Bound of Sum of Square Roots Problem

In [1], Garey et al. identify what would later be known as the Sum of Square Roots Problem in the course of working out the NP-completeness of Euclidean TSP. Given integers $a_1, a_2, \ldots, a_n$ ...
4
votes
3answers
282 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 ...
18
votes
7answers
1k views

Books/Lecture Notes on Parametrized Complexity

I would like to learn about Parametrized Complexity (both on the algorithmic side and on the hardness side). What books/lecture notes can I read on this subject?
4
votes
2answers
146 views

reference request for construction of expanders

I'm looking for a good exposition of the explicit constructive proof of the existence of expander graph families due to Reingold Vadhan and Wigderson. Arora/Barak has a chapter on it, but i find it ...
2
votes
0answers
73 views

Common techniques for the acyclic orientation problem under some special constraint?

An acyclic orientation of an undirected graph is an assignment of a direction to each edge(an orientation) that does not form any directed cycle and therefore generates a directed acyclic graph(DAG). ...
-1
votes
1answer
119 views

Gödel-Numbering of the Context-Sensitive Languages

I would like to have a Gödel-numbering of the context-sensitive languages. Because there is no obvious syntactic distinction between LBAs and TMs, I cannot number the former in an immediate way. So I ...
2
votes
0answers
106 views

Book recommendation treewidth

I am searching for a good book (or survey paper) on treewidth. I would be delighted if the book/paper surveys multiple approaches to treewidth (eg: structural, algorithmic, `language-theoretic') and ...
3
votes
1answer
135 views

The theory of definitions in first order logic

I'm looking for a clear and thorough treatment of the theory of definitions in first order predicate logic from a syntactic/proof theoretic point of view (as opposed to semantic/model theoretic point ...
4
votes
1answer
106 views

A first order logic extended with binding terms like the familiar set descriptors $\{x:\varphi\}$

First order logic comes equipped with two kinds of terms: Variable: those terms of the form $x$ for some variable $x$, of which there are infinite. Function application: those terms of the form $f(...
5
votes
0answers
178 views

Generalization of Element Distinctness

In the element distinctness problem, one has query access to an arbitrary multiset of $n$ elements and must decide whether they are all distinct. From a property testing point of view, the question ...
7
votes
0answers
233 views

Reverse Skolemization?

I'm wondering if there are any references on "reverse skolemization", that is, converting a formula with functions into one purely consisting of quantifiers by eliminating function applications. I'm ...
2
votes
1answer
122 views

Lower bound on the worst-case unbiased coin flips to sample a distribution?

Say that we have a distribution $\mathcal{D}$ such that all probabitilities associated with it are $p$-bit fixed precision numbers, so: $$ \Pr_{X\sim \mathcal{D}}[X = k] =\sum_{i = 1}^p \frac{k_i}{2^i}...
5
votes
1answer
166 views

Does the following type of hitting problem have a name?

Given a ground set, say $[n]=\{1,2,\dots,n\}$, and a collection of subset families $\mathcal F_i\subseteq 2^{[n]}$, $i=1,2,\dots,m$, I want to select $m$ sets $B_i\in\mathcal F_i$ such that the ...
2
votes
1answer
92 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 ...
4
votes
1answer
221 views

Looking for reference on NP-Completeness of proofs of length n

Given a deductive system $\Lambda$, and some well-formed-formula S, one can ask the question "Is there a proof S in $\Lambda$ of length n?" If n is presented in base-1 and if all the axioms of $\...
3
votes
0answers
53 views

Algorithms for Maximum weight connected subgraph in planar graphs

I wonder what is known about the two following maximisation problems. Maximum weight connected subgraph : Input : A graph $G$, with weights $w_v\in \mathbb{R}$ for each vertex $v \in V(G)$ Output :...
12
votes
1answer
395 views

Deterministic error reduction, state-of-the-art?

Assume one has a randomized (BPP) algorithm $A$ using $r$ bits of randomness. Natural ways to amplify its probability of success to $1-\delta$, for any chosen $\delta>0$, are Independent runs + ...
0
votes
0answers
26 views

Two question regarding coreset construictions

I have two questions regarding coreset construction of clustering problem In A Unified Framework for Approximating and Clustering Data, a very general framework is given to construct coresets for ...
0
votes
0answers
57 views

Linear time algorithm for projective clustering

There is a lot of work in clustering of high dimensional data. In case of k-means, it is shown here that one can get an $(1+\epsilon)$-approximation in linear time, yielding a PTAS, by random sampling....
16
votes
2answers
1k views

“Almost sorting” integers in linear time

I am interested in sorting an array of positive integer values $L = v_1, \ldots, v_n$ in linear time (in the RAM model with uniform cost measure, i.e., integers can have up to logarithmic size but ...
5
votes
1answer
102 views

k-testable languages with non-constant k?

Let $p_t(w)$ and $s_t(w)$ denote the prefix and suffix of length $t$ of the word $w$, respectively. If $|w| < t$, then $p_t(w) = s_t(w) = w$. Furthermore, let $i_t(w)$ be the set of infixes of ...
3
votes
0answers
50 views

Hardness of Approximation of Set Cover with Growing Size Bound

I'm considering the minimum set cover problem with the constraint that each set contains at most $k$ elements. Here, $k$ depends on the size of the universe. For example, $k$ may equal $\log n,\sqrt ...
7
votes
1answer
75 views

Simple proof that splay trees have the dynamic finger property?

Splay trees are conjectured to be dynamically optimal, and they're known to have a number of nice properties, including the dynamic finger property, which says that the amortized cost of an access in ...
5
votes
1answer
116 views

Complexity of propositional LTL with past operators and freeze quantifier?

In "A Really Temporal Logic", by R.Alur and A.Henziger, they introduce an extension of Linear Temporal Logic with a freeze quantifier $x.\phi$, which allows to "give a name" to the current time point ...
5
votes
0answers
51 views

Hardness result or reference for optimal Gaussian elimination process

I'm wondering if the following problem is NP-Complete or has any hardness result. References on related problem are also welcome. Input: integers $n\geq1,k\geq0$ and an invertible matrix $M\in\...
8
votes
1answer
262 views

Is there any quantum analog of the VP vs. VNP problem?

From Wikipedia: $\mathsf{VP}$: The class VP is the algebraic analog of P; it is the class of polynomials $f$ of polynomial degree that have polynomial size circuits over a fixed field $K$. $\...