Questions tagged [reference-request]

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

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Error analysis of Estrin's method

Estrin's Method is an alternative to Horner's method for evaluating polynomials. To evaluate a polynomial $P(x)=\sum_{i=0}^7 a_i x^i$ at a point $x\in\mathbb R$, it first computes the powers $x^2$ and ...
4 votes
1 answer
186 views

Relationship between the transition monoid of an automaton and its adjacency matrix

Let $A=(Q,\Sigma, \Delta, q_0, F)$ be an NFA over an alphabet $\Sigma$, $M(A)$ be its transition monoid. For all $a\in\Sigma$, let $S_a\in\mathbb{B}^{|Q|\times|Q|}$ be the adjacency matrix of $A$ ...
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16 votes
0 answers
226 views

Can we do integer addition in linear time?

Why, yes, of course. But I'm actually interested in the cost of computing the sum of multiple integers: Input: A sequence of nonnegative integers $\langle X_i:i<k\rangle$ written in binary. Output: ...
5 votes
1 answer
142 views

Stronger "induction" principles than induction-recursion

Are there type theories in the literature with "induction" principles stronger than induction-recursion? This answer gives System F as an example of a theory stronger than MLTT + induction-...
3 votes
0 answers
62 views

Exponential version of $CC^0$

(In this question, "uniform" will mean $DLOGTIME$-uniform.) In Allender's 1998 paper "The Permanent Requires Large Uniform Threshold Circuits", he talks about the "exponential ...
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3 votes
1 answer
124 views

Treewidth for hypergraphs that specify connectedness requirements

This question is about an alternative definition of treewidth, called weak treewidth. It is defined on hypergraphs where hyperedges intuitively require that the connected subtrees of occurrences of ...
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3 votes
0 answers
67 views

Bounding the size of a power of a proper interval graph

Is there a citable proof of the following result (or perhaps a generalization of it)? Lemma 1. Let $G=(V, E)$ be a proper interval graph. Let $G^k=(V, E^k)$ be the $k$th power of $G$. Then $|E^k| = ...
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1 vote
2 answers
189 views

How much information does it take to specify, not each member of a group, but any one member?

It takes exactly $\log_2 n := \lg n$ bits of information to specify a number from $\{1,2,\ldots,n\}.$ Likewise, it takes $\lg{n\choose s}$ bits of information to specify a subset of $s$ out of the $n$ ...
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3 votes
0 answers
88 views

Succinct problems over uniform computational models

For a language $\Pi$, the traditional definition of "Succinct-$\Pi$" is the set of encodings of circuits whose truth tables are members of $\Pi$. This definition is essentially restricted (...
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1 vote
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Alternative notions of bisimulation

Suppose $(S, \Lambda, \rightarrow)$ is a labeled transition system. A bisimulation is a relation $R \subseteq S \times S$ s.t. $\forall \alpha \in \Lambda$ and $\forall p, q \in S$ with $R(p,q)$, $\...
2 votes
0 answers
103 views

Faster algorithms to estimate the subset sizes

Lemma: Consider two sets $B ⊆ U$, where $n = |U|$. Let $ξ, γ ∈ (0, 1)$ be parameters, such that $γ < 1/ \log n$. Assume that one is given an access to a membership oracle that, given an element $x ∈...
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2 votes
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Algorithms for parametric matroid optimization

Let $M$ be a rank $r$ matroid with basis set $\mathcal{B}$ and an independence oracle. Given a linear function $w_e$ on each element $e$ of the matroid, we want to find the minimum weight basis for ...
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0 votes
0 answers
53 views

Uniformly redistributing items across bins. What problem is this?

I'm trying to find reading material on a particular problem I'm interested in, but I don't know the terms to search. Problem assumptions/definitions: We have finite number of items I with weights [0, ...
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1 vote
0 answers
104 views

Fastest algorithm for non-empty bins

Assume we have $n$ bins, and exactly $k>0$ of them, are non-empty. Furthermore, assume that we can check if a specific urn is empty in constant time. I am looking for a randomized algorithm that ...
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2 votes
0 answers
49 views

Has there been any research on faster tensor inner products?

Matrix multiplication is a well studied problem which is recently back in the news due to deepmind. That got me wondering has anyone looked at the more general problem of faster tensor multiplication? ...
1 vote
0 answers
45 views

Diameter queries for stream of points

Given an online stream of $k$ points $x_1, x_2,\ldots,x_k$ with $x_i \in \mathbb{R}^2$. By online we mean that when $x_i$ arrives we have no knowledge of points $x_j$ for $j > i$. Denote by $S_i$ ...
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3 votes
0 answers
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Modelling channels without specifying input alphabets

The standard mathematical model of a communication channel is that of a stochastic matrix $(C(x|a))_{a \in A, x \in X}$, where $A$ is the input alphabet and $X$ the output alphabet. This definition ...
4 votes
0 answers
73 views

Lower bound on the size of Skolem functions

Consider a quantified Boolean formula $f$. We can convert it into Skolem Normal Form formula $f^*$ such that $f$ is satisfiable iff $f^*$ is satisfiable, by replacing variables that are existentially ...
0 votes
0 answers
59 views

Examples of Gaussian randomized algorithms

I've been thinking about algorithms of the form where a quantity $c$ can be viewed as the expectation of some estimator (random variable) $X$ and the expectation is taken over some multivariate ...
2 votes
1 answer
70 views

Dual of cut of embedded graph disconnects surface

Let $G$ be a graph that embedded on a surface of genus $g$, moreover the embedding is triangulated. Let $C$ be a collection of edges that forms a minimal edge cut for $G$. Let $C^*$ consist of the ...
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0 votes
0 answers
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Quantifying the cost of procedures

Is there any research on quantifying the cost of a procedure, with regard to compiler optimization? I.e. assigning some kind of cost in terms of CPU time or memory to a procedure, either so the ...
4 votes
0 answers
88 views

Time Complexity of Pairwise Graph Connectedness

The Setup Consider the following algorithmic problem which, for now, I will call $\mathsf{2GraphConnector}$. Input: A natural number $|V|$, and a finite collection $\mathscr{E} = \left\{E_1, E_2, \...
0 votes
0 answers
94 views

Faster algorithm for sampling unifromly at random

The goal is to come up the simple data structure for sampling a uniform point from a collection of sets, i.e., given a sub-collection $\mathcal{B}$, sample a point in $\cup \mathcal{B}$ uniformly at ...
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3 votes
0 answers
48 views

Reference for cost of translating between regular language formalisms

It is well-known that regular languages can be defined equivalently via many formalisms, among which regular expressions, NFAs, finite monoids, Monadic Second-Order logic (MSO). The cost (say in size ...
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2 votes
1 answer
192 views

Are there research papers on related to algorithm fairness in theoretical computer science?

I have seen several articles related to algorithmic fairness in machine learning and AI. I am not able to find out research paper on algorithm fairness in theoretical computer science. Kindly suggest ...
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3 votes
0 answers
84 views

Linear time in-place stable sort

Surprisingly, linear time in-place stable sort is possible with integer keys of $O(\log n)$ bit length. An algorithm appeared in Radix Sorting With No Extra Space (Franceschini, Muthukrishnan, ...
1 vote
0 answers
113 views

How to measure the weirdness of algorithms?

Let $M$ is a polynomial $k$-tape Turing machine and $C^t(x)$ is a time-bounded Kolmogorov complexity. Let $str_M(x)$ be a string of the following form: $$str_M(x)=w_1^1\# w_2^1 \# ... \# w_{m}^1 ■ w_1^...
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1 vote
0 answers
57 views

The tree augmentation problem, but with hyperlinks

In the (Weighted) Tree Augmentation Problem, we are given a tree $T = (V,E)$ and a set of additional edges $L$ called links with non-negative costs. Each link $\ell = (u,v)$ covers the tree edges ...
0 votes
0 answers
51 views

Publications on left recursion and PCRE regex engine

Is there any paper (or at least technical report / preprint or even thesis) mentioning that regex engines cannot match expressions that contain "left recursion" (explained below)? I am ...
5 votes
0 answers
98 views

Data structures to store monotone functions

I am looking for approaches storing strictly increasing natural-valued functions defined on a (subset of) $[0..N]$: $$ \forall x \in X: 0 \le x \le N\\ f: X \to \mathbb N\\ \forall x,y\in X:\quad x<...
4 votes
2 answers
159 views

How exactly does a compatible reduction relation change the $\pi$-calculus?

The reduction relation given for the $\pi$-caculus is usually not compatible (i.e., it's not preserved under arbitrary contexts). Quoting Milner's The Polyadic $\pi$-Calculus: A Tutorial: It is ...
1 vote
0 answers
112 views

Can we describe any context-sensitive language by a grammar without left recursion?

The main question: is it possible to avoid left recursion in a context-sensitive grammar (see example below), i.e., if for any context-sensitive language $L$, there exists some context-sensitive ...
6 votes
0 answers
81 views

Relationship between natural deduction refutation and tableaux for propositional logic

Which kind of relationship is there between natural deduction refutations of a set f propositional logic assumptions, and the corresponding tableaux? For example, consider the unsatisfiable set $\...
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0 votes
0 answers
49 views

Solving sampling problems with circuits?

If I allow a circuit family (say, poly size, polylog depth) poly($n$) bits of randomized advice, then I can ask if its output samples from certain distributions or not. However I don't know what the ...
9 votes
1 answer
1k views

Are there survey papers in theoretical computer science?

Are there conferences or journals where we can publish surveys/literature review papers related to theoretical computer science problems? If provide a list of such conferences and journals. I know ...
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4 votes
0 answers
76 views

Are there classes for that FO-model checking is FPT on hypergraphs?

For graphs, there are many classes that admit FPT-algorithms for model checking of first order logic, e.g. the class of nowhere dense graphs by Grohe et. al. Are there similar results for ($k$-uniform)...
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2 votes
0 answers
90 views

Reference for complete problems for $FNP^{NP}$

I'm looking for a reference for complete problems for $FNP^{NP}$, i.e., the class of functional problems solvable by a polynomial time non-deterministic Turing machine that has access to an $NP$-...
2 votes
0 answers
61 views

Pebble games and conversions to bounded width circuits

Questions: Are there references which mention the relation between pebble games and conversions to bounded width circuits? Here, "conversions to bounded width circuits" means that circuits ...
1 vote
0 answers
61 views

Code indistinguishability assumption for Code based cryptography (in special cases)

Cryptosystems that are based on error correcting codes are often based with hardness of the two problem. Computational syndrome decoding is hard Indistinguishability Assumption (IA): Distinguishing ...
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2 votes
0 answers
73 views

From formal models to programs - Model Checking

I am reading on Automata, Model Checking and CTL/LTL. I am looking for examples/references/books that help me understand the following: Given a program (for example Python or Java), how can I change ...
0 votes
0 answers
28 views

Minimax computation for classification problems with smooth densities functions

Fix $d=1$, $r \in (0,\infty)$ and a neigborhood $\Omega$ of $0$ in $\mathbb R^d$ and let and let $W^{1,\infty}(r)$ be the Sobolev ball continuously differentiable functions $f:\mathbb R^d \to \mathbb ...
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0 votes
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70 views

Algorithms with advices of huge precomputed data

My main interest is complexity theory, and I'm studying the large or huge advice of Turing machines in the ongoing work. As related to the study, I'm wondering what's known about "precomputation&...
2 votes
2 answers
148 views

Seeking references on writing a long string $\ell$ as concatenation of shorter strings $s_1, s_2, s_3, ...$

Given: a (long binary) string $\ell$, and a set of (short) strings, $s_1, s_2, ...$ . Can $\ell$ be written as concatenation of the short strings? I am looking for references on: the name of the ...
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5 votes
1 answer
163 views

Establishing competing memory limits for pushdown automata

Let $L$ be the language of all even-length strings whose first half is a palindrome. Let $L$ be the language of all even length strings whose first half is imbalanced—with an unequal number of $\...
0 votes
0 answers
81 views

Programming languages with constraints on values of variables?

Hi Theoretical Computer Science Stack Exchange, I have been wondering if there are programming languages where one can have constraints on values variables can have? Have such approach been used in ...
0 votes
0 answers
21 views

2-connectivity of dual of a minimal cut in a bounded genus graph

Let $G$ be a graph of genus $g$ embedded on a surface of genus $g$. Let $s,t \in V(G)$. Consider a minimal $s,t$-cut $C$ in $G$. Let $H$ consist of the union of faces adjacent to $E(C)$. Notice that $...
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1 vote
0 answers
32 views

Interval arithmetic adapted to backwards stable problems

In numerical analysis, there are algorithms which are either forwards stable or backwards stable. Forwards stability is strictly stronger, and is more desirable. Unfortunately, it is in many instances ...
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8 votes
1 answer
164 views

Word equations with integer parameters

This is mainly a reference request. Let us define a parameterized expression on a finite alphabet $\Sigma$ as follows: $$e,e':= w\mid w^i \mid e\cdot e'$$ Where $w\in\Sigma^+$ is a word, and $i$ is an ...
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0 votes
1 answer
56 views

Are there logical devices similar to "existential variables" or "blank nodes" of Semantic Web?

In Semantic Web, alongside permanent names of things also "temporary names" named "existential variables" or "blank nodes" denoted as "_:label" are used. All ...
3 votes
1 answer
94 views

Name for set of vertices that are pairwise within distance two

A 2-stable set (or a distance-two independent set) of a graph $G$ is a set of vertices which are pairwise at a distance greater than 2 in $G$. Is there a name for a set of vertices which are pairwise ...

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