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Questions tagged [reference-request]

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

5
votes
1answer
134 views

For which $R$ is $\{0^a10^b10^c\mid R(a,b,c)\}$ context-free?

Unless I'm mistaken, a language of the form $\{0^a10^b\mid R(a,b)\}$ is context-free if and only if $R$ is a finite union of linear (in)equalities involving integer constants and the variables $a$ and ...
2
votes
1answer
67 views

Automata as term rewriting systems

It came to my mind that automata (say to start DFA) can be thought as a special kind of rewriting systems. So if one has a word w , one tries to reduce it to the $\epsilon$ word. In other words ...
0
votes
0answers
56 views

Coordinate descent in integer programing: when does it work?

Denote $N_i=\{0,1,\dots,\bar{n}_i\}$ and define $N=N_1\times \dots \times N_I$. I want to minimize a function $f:N\rightarrow \mathbb{R}$. It is very easy to minimize $f$ coordinate by coordinate so ...
6
votes
0answers
136 views

Immutable Space Model

I have heard it said that time is more precious than space because we can reuse space but not time. What if we treat space with this much reverence? What is generally known about models of ...
3
votes
0answers
161 views

What is a good route for a math student to self study computer science systematically and efficiently?

I decided to ask this question after being attracted by how much one can do with the knowledge in computer science, including iOS application development, game(or mods) development, website creating, ...
-3
votes
1answer
59 views

Soundness of type (systems)

For someone without strong background in theoretical computer science: can soundness be a property of a type (given a type system), or a property of type systems only? In other words, can we say that ...
219
votes
37answers
106k views

What Books Should Everyone Read?

[Timeline] This question has the same spirit of what papers should everyone read and what videos should everybody watch. It asks for remarkable books in different areas of theoretical computer ...
97
votes
37answers
13k views

What are the recent TCS books whose drafts are available online?

Following the post What Books Should Everyone Read, I noticed that there are recent books whose drafts are available online. For instance, the Approximation Algorithms entry of the above post cites ...
1
vote
0answers
37 views

Optimally fair stable matching

There's a nice post by Gil Kalai which outlines the inherent bias in stable matching algorithms quantitatively. In the traditional loyd shapeley algorithm for $n$ men and $n$ women, given randomly ...
13
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?
10
votes
0answers
225 views

Have people looked for parameterized algorithms for problems that are not in NP?

Are there problems that are not in NP (e.g., NEXP-complete problems) but admit FPT algorithms for a reasonable parameterization (and specifically, the standard parameterization of a problem -- the ...
2
votes
0answers
177 views

BQNC and Abelian Hidden Subgroup Problem

We know integer factorization is in $BPP^{BQNC}$ from Cleve and Watrous. Is Abelian Hidden Subgroup Problem also in $BPP^{BQNC}$? In particular is Discrete Logarithm in $BQNC$ or at least in $BPP^{...
13
votes
4answers
724 views

Modeling objects (OOP) in dependent type theory

I am interested in modeling objects, from object oriented programming, in dependent type theory. As a possible application, I would like to have a model where I can describe different features of ...
2
votes
1answer
319 views

Is there a counterexample to this work?

Is there a counterexample to this claim https://arxiv.org/abs/1610.00353? They claim a $O(n^6)$ LP model with simulations to support. I think asking validity is not a reasonable problem. However ...
0
votes
0answers
37 views

What is the right term/theory for prediction of Binary Variables based upon their continuous value?

I am working with a linear programming problem in which we have around 3500 binary variables. Usually IBM's Cplex takes around 72 hours to get an objective with a gap of around 15-20% with best ...
3
votes
1answer
197 views

Finding self-similar homomorphisms of a FSM transducer

Consider a special case of homomorphisms of FSM transducers (or "generalized sequential machines" in [1]). Let $F$ be a transducer accepting a language $L$, and let $h(x)$ be a homomorphism function ...
1
vote
0answers
38 views

A categorized (?) list of functional pearls in JFP and ICFP

Is there a list of (categorized preferred) functional pearls ever published in ICFP and JFP? I could go to the ICFP proceedings and JFP issues and find all of them, but this would be time-consuming. ...
9
votes
2answers
249 views

Hereditary substitution with a universe hierarchy

I've read about hereditary substitution for the Simple Lambda Calculus and for The Logical Framework with distinct terms and types. I'm wondering, are there any examples of hereditary substitution in ...
3
votes
0answers
55 views

Problems and theories in CS that uses Fibonacci numbers

I want to know problems and theories where Fibonacci sequence is used and where we have some possibility to use Fibonacci numbers. I have found that- In counting number of steps for Euclidean ...
1
vote
1answer
381 views

Possible to do Complexity theory with only counting and Pigeonhole

Most of the proofs in the book Computational complexity by Barak and Arora seem to be Pigeonhole in disguise. What are some places in Complexity theory where counting and Pigeonhole was insufficient ...
6
votes
1answer
159 views

Does Max Planar 3-SAT admit a PTAS?

Suppose we are given a formula $\phi$ of 3-SAT, with variables $x_1,\dots, x_n$ and clauses $C_1,\dots, C_m$. Consider the graph $G_\phi$ where there is one node for each clause $C_i$, for each ...
5
votes
0answers
141 views

Classification of randomized approximation algorithms

Is there a known classification of randomized approximation algorithms, in the same vein as the distinction between Monte Carlo and Las Vegas algorithms for decision problems? (Or equivalently ...
9
votes
1answer
125 views

Best known asymptotic PCP sizes / 3-SAT

What are the best known asymptotic upper bounds on sizes of probabilistically checkable proofs? Ideally, I am looking for a contemporary survey on this broad question, but if there is none, I am ...
5
votes
2answers
290 views

Preservation under Substitution with Telescopes

In the simply typed lambda calculus, one can show the following result, known as "preservation under substitution": If $\Gamma \vdash v : \tau_1$ and $(x : \tau_1) \vdash t : \tau_2$, then $\Gamma \...
11
votes
1answer
1k views

Given a PDA M such that L(M) is in DCFL construct a DPDA N such that L(N) = L(M)

Is it possible to construct an algorithm which takes as input a pushdown automaton $M$ along with the promise that the language accepted by this automaton $L(M)$ is a deterministic context-free ...
7
votes
2answers
206 views

Reference request: Skeptics of classical threshold theorem

Early classical computing had skeptics, or at least cautious researchers, that were skeptical reliable computing results were possible. Scott Aaronson references this in a page on his site: A: The ...
8
votes
1answer
145 views

What's the difference between Moggi's computational metalanguage and Moggi's lambda calculus?

This is a reference confusion. Sometimes I see people use the term "Moggi's computational metalanguage" to refer to the calculus presented by Moggi, and sometimes to "Moggi's computational lambda ...
10
votes
1answer
263 views

Is the Kolmogorov complexity of the truth tables of the halting problem known asymptotically?

Let $HALT_n$ denote the string of length $2^n$ corresponding to the truth table of the halting problem for inputs of length $n$. If the sequence of Kolmogorov complexities $K(HALT_n)$ were $O(1)$, ...
9
votes
1answer
394 views

Proof techniques for showing that dependent type checking is decidable

I'm in a situation where I need to show that typechecking is decidable for a dependently-typed calculus I'm working on. So far, I've been able to prove that the system is strongly normalizing, and ...
24
votes
8answers
4k views

Computing the Levenshtein distance quickly

Given a huge database of allowed words (alphabetically sorted) and a word, find the word from the database that is closest to the given word in terms of Levenshtein distance. The naive approach is, ...
3
votes
2answers
122 views

Examples/Textbooks on amortized analysis of algorithms

I am trying to get the amortized analysis for a complicated algorithm. I am wondering whether there are textbooks or illustrative examples that could serve as inspiration of techniques in amortized ...
5
votes
1answer
177 views

Boolean circuits which correspond to L/poly

Branching programs are usually used as a computation model for non-uniform logarithmic space $\mathsf{L}/\mathrm{poly}$. Is there a reference about Boolean circuits corresponding to $\mathsf{L}/\...
9
votes
1answer
260 views

Are there protein-based computational models?

Is there an framework/formalism which defines computational models based on proteins other than Adleman's DNA model or this work by Cherry and Qian?
9
votes
1answer
330 views

“Verifiable information”: is this a known concept?

The following seems to me like a natural definition and I wonder whether it's been studied somewhere Consider $\mathsf{X} \subset 2^{\lbrace 0, 1 \rbrace^*}$ a set of languages. Then $K \subset \...
13
votes
0answers
252 views

Algebraic topology for termination proofs

I'm reading about various ways in which termination proofs of software verifiers are built: ad-hoc methods that detect recursions, term-rewriting, synthesis of lexicographic orderings... From the ad-...
4
votes
3answers
122 views

Complexity of isotopy of embedded graphs

I am looking for previous work on the following problem: given two graphs embedded in the plane without crossing, determine if they are isotopic. By isotopic I mean that there is a continuous ...
-1
votes
1answer
66 views

How to know if a problem is distributable?

I am new to the world of Parallel computing and that is why don't know exactly where I should look at or search to get the answer. Is there any theorem or just general theory determining which code ...
5
votes
1answer
120 views

If $u\cdot v \in (z \cdot z')^*$ and $v \cdot u \in (z' \cdot z)^*$ then $u \in (z \cdot z')^* \cdot z$

I'm searching for a reference for the following property: Fact. Let $u, v \in A^*$. Write $w$ for the primitive root of $u\cdot v$, i.e., $u\cdot v = w^c$. There are unique words $z, z'$ such ...
16
votes
1answer
188 views

Which monotone Boolean functions are representable as thresholds on sums?

I will introduce my problem with an example. Say you are designing an exam, which consists of a certain set of $n$ independent questions (that the candidates can get either right or wrong). You want ...
9
votes
2answers
146 views

Decidability of type inference and type checking in MLTT

In Martin-Löf's An Intuitionistic Theory of Types: Predicative Part it is proved that type checking $a \colon A$ is decidable subject to $a$ being typeable in the first place, by proving a ...
5
votes
1answer
260 views

Is there a useful notion of being “approximately computable”

It seems that we can define a notion of being “approximately computable” where a set, $S$, is approximately computable if there is a family of computable functions $f_n(x)$ such that $$\lim_{n\to\...
16
votes
0answers
416 views

An algebra of complexity classes

A key feature of unrelativized computation is its composability out of smaller fragments, and to partially capture the composability, I came up with an algebra of fine-grained complexity classes. For ...
5
votes
3answers
443 views

Sorting a programs instructions until it works

Lets say I have a computer program below. (define (factorial x) (if (= x 0) 1 (else (* x (factorial (- x 1))))) I then take each line of the ...
11
votes
0answers
233 views

Inapproximability of multiterminal cut

In the multiterminal cut the input is a graph $G$ and a subset $T$ of its vertices. The task is to remove the minimum number of edges from $G$ such that there is no path connecting any distinct ...
10
votes
1answer
236 views

Algorithms on graphs represented using BDDs

The simplest representations for graphs use adjacency matrices/lists, meaning that each node and edge is explicitly represented. The importance of implicit representations for graphs exhibiting strong ...
3
votes
1answer
113 views

Rademacher complexity for piecewise-linear convex function

Consider a function family $$\ell(x)=\max_{1\leq k\leq K} a_k^\top x + b_k,$$ where $a_k,b_k \in \mathbb{R}^d$ are bounded in the sense of some norm and $K\geq 2$. What is the best upper bound on the ...
9
votes
0answers
98 views

Graphs with minimal-size induced subgraphs

I consider undirected graphs $G = (V, E)$ for which I write $\text{n}(G) := |V|$ the number of vertices and $\text{m}(G) := |E|$ the number of edges. For $d \in \mathbb{N}$, I say that $G$ is $d$-...
6
votes
0answers
65 views

Reference request: transforming a grammar to Greibach normal form preserves the number of parse trees

I believe that most "natural" ways of transforming a grammar to the GNF should preserve the number of parse trees for each string. For example, Urbanek's construction from the paper "On Greibach ...
1
vote
0answers
26 views

Variability of gradient estimates and convergence rate in stochastic gradient descent/ascent

I am aware that convergence in stochastic gradient problems is very sensitive to the variance of your gradient estimator. One issue I'm running into is that the gradient is a random vector and so ...
2
votes
0answers
49 views

For each edge, find a matching that containing it and has maximum weight

Given a weighted graph $G=(V,E)$. For each edge $e\in E$, we are interested in finding a maximum weight matching over all matchings that contains edge $e$. If $G$ is bipartite, then this can be done ...