Questions tagged [reference-request]

Questions requesting papers in the literature on specific, narrow issues.

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22 views

Searching for sorting algorithm taking into account all possible solution of similar numbers

I need a reference for sorting algorithm where all possible orders are considered. example: if we have four values of n, and we do know there values n1(3) n2(5) n3(5) n4(10) and want to order them in ...
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Control Flow Graph - How to represent returns in code

Consider the following program int someCode1(int x){ if (x < 0) return 0; else return x; Last Statement;} Last statement could be either "printf(...
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Are there any references for this theorem of Lercher?

Let $\Delta = \lambda x.(x)x$ and consider $\Omega = (\Delta)\Delta$. Then $\Omega$ is exactly the only $\lambda$-term of the form $(\lambda x.t)v$ such that $(\lambda x.t)v=t\{v\ /\ x\}$. Does ...
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Modern standard texts on distributed systems

I'm starting a job soon that involves a large number of disciplines interacting at once. I'm knowledgeable in most of these areas; at least enough that when I don't know something I know how to look ...
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1answer
35 views

Online Taylor series calculator

When I compute the the eigenvalues of the matrix $$\begin{bmatrix}x^3& 2 + x^3& 3 - 2 x^3\\ 2 + x^3& 4 - 5 x^3& 5 + 3 x^3\\ 3 - 2 x^3& 5 + 3 x^3& x^3\end{bmatrix}$$ using ...
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99 views

Multivariate piecewise linear interpolation

I am looking for a reference to a solution of the multivariate piecewise linear interpolation. I am not quite sure how to generalize a well-known dynamic programming Segmented Least Squares algorithm. ...
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1answer
36 views

What is the anayslsis that a heap's optimal branching factor is 2 <= factor <=5?

I'm reading the book Advanced Algorithms and Data Structures and it makes the claim that the optimal branching factor for a heap is 2 <= D <= 5 and that it is ...
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3answers
94 views

Do modern computers prevent instructions being executed by audio? If so, how?

Most know that early phones and modems, and still, fax machines, sent information through the use of tones. This got me thinking - could audio be a viable vector for executing instructions by a bad ...
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1answer
30 views

Arithmetic hierarchy via oracles

My professor gave an introduction to the arithmetic hierarchy via Turing reductions, stating that, for instance, $\Sigma_2 = \text{r.e.}^\text{r.e.}$ (namely an $\text{r.e.}$ pseudocode with access to ...
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1answer
25 views

Heuristics for a variant of the traveling salesman problem

I am looking at a variant of TSP in which rather than visiting every node, there is a given collection of (possibly overlapping) subset, and the salesman must pass through one node from each subset. ...
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Intro to basic automated proof search for theorems in equational theories

I have heard about this topic, and I'm merely looking for a reference that I can read through: I know about formal logic as a proof-checking system, but I haven't yet learned about actual algorithms ...
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40 views

List of algorithms that depend on sorting / ranking / argsorting

I am looking for a list of algorithms that depends on sorting / relative ranking / argsorting, not for a list of sorting algorithms. I want to study and illustrate the importance of fast sorting in ...
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2answers
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Mathematical models of computation that capture more advanced OS and CPU design features

The universal Turing machine is the standard theoretical model of a stored-program computer. While in one sense as general as possible (Turing completeness), it doesn't explicitly contain many of the ...
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Is there a book with 100 reductions?

In a lecture I'm taking about complexity theory a professor said, there are infinite many NP-complete problems. Question: I was wondering if there exists something like a database or a book with some ...
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30 views

Periodic 4D Triangulations

I am looking for references and/or algorithms for generating 4-dimensional periodic triangulations on unit 4 lattices. That is, generating a space filling triangulation of the 4D integer lattice (Z^4) ...
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178 views

Produce a Dynkin system from a finite set of finite sets

[Updated question] A Dynkin System is, provided all sets are finite, a collection of subsets of a universal set closed under complements with the universal set and closed under union of disjoint sets. ...
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1answer
59 views

what precisely do linear types prevent?

"A theory of type polymorphism in programming" introduced the Hindly-Milner type system whose punchline can be summarized "well-typed terms don’t get stuck". They do this by ...
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1answer
32 views

Using B+Tree to implement index, when the index-key size and the data-block size are of the same order

I want to implement an Index using a B+Tree as the underlying data structure. The index will have to support key sizes which are of order of my block size, what means I cannot save all the key as a ...
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35 views

Kolmogorov complexity of probability distributions, with and without time bound

Kolmogorov complexity of a string is the length of the shortest algorithm that generates it. Here I'm focusing instead on randomly distributed strings $x$, with length $n$, with a probability ...
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1answer
28 views

Counter automata with a bound on the counters?

It is widely known that emptiness of counter automata is undecidable since two counters are enough to simulate a Turing machine (see the classic book from Hopcroft and Ullman, for example). However, ...
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1answer
44 views

What is this linear optimization problem?

Given a $d$-dimensional vector $v = (v_1,\dots,v_d) \in \Bbb{R}^d$, we define $f(v) = \min_{i\in [d]} \{v_i\}$ to be the smallest coordinate of $v$. Let $v^1,\dots,v^n \in \Bbb{R}^d_{\ge 0}$ be non-...
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1answer
47 views

Filling in the image by the brain

The Cones and rods are not evenly or precisely sensitized on the retina by incoming light. Because of this, the image is formed with distortions. But the brain corrects these deformations through a ...
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1answer
38 views

Definition of static property of object in OOP

Grady Booch in Object-Oriented Analysis and Design with Applications says: The state of an object encompasses all of the (usually static) properties of the object plus the current (usually dynamic) ...
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1answer
141 views

Proving FPT is strictly contained in XP

In their book Fundamentals of Parameterized Complexity, Downey and Fellows claim (in chapter 27.1) that $\mathrm{FPT}\subsetneq \mathrm{XP}$, and that this is a "basic result" that follows ...
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4answers
134 views

A beginner book on algorithms

I am a tenth grader. I currently learnt about sorting algorithms in java in school. I started with the book "Algorithmic Mathematics" so as learn about algorithms mathematically. I know very ...
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2answers
120 views

Is there a good algorithm to divide two integers without using division directly?

Problem. Given positive integers $a$ and $b$, obtain $\frac{a}{b}$ without using division ($/$) directly, though addition ($+$), subtraction ($-$), multiplication ($\times$) and bit-shifts ($\gg$ and $...
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1answer
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What is the primary reference for the observation/discussion of how neural networks struggle with ambiguous training datasets?

It is known that neural networks, such as convolutional neural networks, struggle with pattern recognition if training sets contain ambiguities (i.e. several labels can correspond to one and the same ...
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1answer
22 views

Convergence of graph neural networks (GNNs)

I'm new to the area, and we don't have a course on graph neural networks at our university. However, I will still like to know the main theoretical results when considering convergence of graph neural ...
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2answers
213 views

Why did finite-state controller with datapath win?

I just finished watching the 1986 SICP lectures, and the concepts are rolling around in my head. My question: why is "finite-state controller with datapath" the implementation of computer ...
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2answers
44 views

What's the error about the definition of NP?

Many sources (including Wolfram's MathWorld) say that NP problem is defined as a decision problem "verifiable in nondeterministic polynomial time" (check Google to see more sources). But ...
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1answer
40 views

How to search all possible combinations for a product?

I'm looking for the name of the problem stated below or, if available, even the algorithm to solve it. This is a hypothetical idea of mine, I don't actually have the necessary data to implement it. ...
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1answer
37 views

Generalization of Cellular Automata

So in the little I know about formalization of cellular automata, it appears there are 4 major categories of cellular automata: 1-dimensional (cellular automata on the line) 2-dimensional (cellular ...
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0answers
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Video lectures about Information Theory and Thermodynamics!

I'd like to know if there is any video courses that relate information theory and thermodynamics, e.g. courses cover laws of thermodynamics, Shannon's entropy, Kolomogorov Complexity, Landauer’s ...
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Calculating ring inequalities with fixed precision

Suppose we are given $n$ $M$-bit (the word size of the computer) integers $x_i$, and wish to calculate a linear or nonlinear inequality involving the numbers (an expression made up from the $x_i$, ...
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1answer
42 views

Existence of good error correcting codes

I recently asked this question and got an answer from Yuval Filmus stating that we can build a solution using error-correcting codes. More specifically, I'm looking for error correcting codes (for ...
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17 views

Edge features in Graph Neural Networks

I would like to know which GNN architectures support edge features, and where can I read about them. If anyone knows where I can search that \ how to distinguish between a GNN that doesn't inherently ...
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1answer
36 views

Is a register machine built out of automata of some sort?

I am looking at register machines like the Random Access Machine. Wikipedia says: Random-access machine (RAM) – a counter machine with indirect addressing and, usually, an augmented instruction set. ...
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2answers
75 views

Silly question: what counts as a "unit of work" when computing big-Oh time complexity

I am going through a fairly non-rigorous textbook called 'Cracking the code interview' and I am bothered by this terminology called "unit of work". It says in the textbook that certain ...
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1answer
63 views

Solving problems by dynamic programming plus quantization to avoid combinatorial explosion

The context: I have been working lately with problems like the following: Let $x_{k}\in\mathbb{R}^n$ be a state evolving accroding to: $$ x_{k+1} = f(x_k,u_k) $$ where $k \in \{ 0,\dots,N-1 \} $, ...
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1answer
17 views

Formal Description Of Data Structure For Infinite Sets Of Reals

The paper I'm working on uses sets as implemented in https://docs.sympy.org/latest/modules/sets.html. A set is stored in a data structure as a sequence of intervals with open or closed bounds, so it ...
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15 views

Research on Tree Automata/Tree Transducers for implementing Tree Generators

I would like to write from scratch a tree pattern matching algorithm. Well actually, not just a matching algorithm, and not even a tree transducer, but a sort of tree constructor that takes basically ...
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1answer
35 views

Uniform convergence for a class of finite dimension

The following theorem is cited in Balcan, M.F., Sandholm, T. and Vitercik, E., 2019. Estimating approximate incentive compatibility which I am currently reading and it is referenced to David Pollard. ...
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4 views

Inferring reward function and transition model from optimal policy

Consider an MDP where the transition model and the reward function are unknown. Consider an optimal policy $\pi^*$ generated from this MDP (say by some oracle who does know the transition model and ...
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19 views

Companion volume to Concurrency verification of Willem-Paul de Roever

At the moment I am working hard with the book "Concurrency Verification Introduction to Compositional and Non-compositional Methods" written by Willem-Paul de Roever et al. In the ...
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Asking for references on errors, testing, system failures etc

I am looking for references that talk about the following subject: Software programs are in general complex systems. That is, if we decompose them into components and we make sure that each component ...
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1answer
27 views

Algorithmic information theory with stochastic algorithms?

Suppose we define a class of algorithms that is allowed to sample i.i.d. Bernoulli bitstrings of arbitrary length, and use these to generate outputs. If we are allowed to use algorithms like this, ...
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15 views

Degree of regularity of a Markov chain

A Markov chain with transition matrix $P$ is termed regular if for some $n$, all entries of $P^n$ are positive. Is there a known notion of degree of regularity quantified in terms of how soon all ...
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28 views

Reliability of information on large social networks like Wikipedia [closed]

I was going through the playlist of an online course on Social Network Analysis offered by the Indian Institute of Technology (Madras), when I came across the claim that "when a lot of people get ...
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1answer
166 views

What is a self-delimiting program?

I came across the term self-delimiting program, referring to the paper "Laws of information (nongrowth) and aspects of the foundation of probability theory" by Levin, 1974. Unfortunately ...
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0answers
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Generalization of finding $L_\infty$ centroid in $R^2$ via rotating and minimizing sum of $L_1$ distances

Given a set of points $x_1, \dots, x_n \in \mathbb{R}^2$, suppose one wants to find: $\text{argmin}_i \sum\limits_{j=1}^{n} \lVert x_i - x_j\rVert_\infty$ i.e. the point which minimizes the sum of the ...

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