Questions tagged [reference-request]

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

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27 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
24 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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47 views

reference request: solving problems by dynamic programming + 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: $$ x_{k+1} = f(x_k,u_k), k=0,\dots,N-1 $$ given some $x_0$ and ...
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10 views

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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1answer
61 views

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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1answer
70 views

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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177 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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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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1answer
54 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
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
30 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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0answers
32 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
43 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
36 views

Problem with understanding Multi-party security circuit for secure stable matching

I am reading the following paper: MPCircuits: Optimized Circuit Generation for Secure Multi-Party Computation Paper Link I have following question: We have two groups shown in the circuit. Why we ...
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1answer
32 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
135 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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1answer
33 views

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
96 views

Where were the ideas of vote, accept and commit phases originally introduced?

In the Stellar Consensus Protocol SCP, the voting procedure follows a 3 phase commit i.e. vote, accept and confirm i.e. see section 5. Is this a novel introduction or has this been previously been ...
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1answer
129 views

Do white box methods for feature extraction exist for facial recognition?

Part of something I'm working on (or rather begin working on) involves white box approaches to facial recognition. I previously worked on something for character recognition using scene segmentation ...
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2answers
116 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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4answers
128 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
204 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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1answer
20 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
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
36 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
16 views

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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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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0answers
23 views

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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16 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
34 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
61 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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2answers
123 views

Minimum set cover with incompatible sets

I'm interested in a variant of minimum set cover where some sets are ``incompatible'' (they can't be chosen simultaneously). To state it more formally: We have a finite base set $X$ and a family $\...
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1answer
16 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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14 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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1answer
264 views

How to translate automatons (Turing machines) into programs of high level programming language?

Every program in high level ("industrial") programming language can be expressed as some Turing machine. I guess, that there exists universal algorithm for doing that (e.g. one can take the ...
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18 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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0answers
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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1answer
100 views

Is there a graph theory textbook that covers treewidth thoroughly?

Can someone recommend a graph theory textbook that covers treewidth thoroughly? Something that focuses on the graph-theoretic structure of bounded treewidth graphs rather than solving problems on them....
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0answers
10 views

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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0answers
14 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 ...
4
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1answer
261 views

What was Robert Floyd's algorithm for inserting brackets?

In page 71 of Mathematics for Computer Science (page 77 in the pdf) it says that "The Turing award (the “Nobel Prize” of computer science) was ultimately bestowed on Robert Floyd, for, among other ...
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0answers
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 ...
2
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1answer
140 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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3answers
4k views

What is the origin of the client server model?

I was wondering if someone knew the origin of the client server model. Where does the term come from (paper, software application, book)?
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0answers
18 views

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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0answers
33 views

Books on Lambda calculus

I would like to learn Lambda calculus (informally). What are the pre requisites for studying lambda calculus ? Can someone recommend an interesting textbook that introduces subject historically with ...
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0answers
20 views

Is there a uniform way of giving for any mathematical formula a hypercomputer that computes it?

Some mathematical formulas directly suggest an algorithm for computing it (even if sometimes an inefficient one). For example, if we recursively define $\sum_{i=1}^nx_i=x_n+\sum_{i=1}^{n-1}x_i$, then ...

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