# Questions tagged [reference-request]

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

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### Compressing grammars by introducing ambiguity and left-recursion

This is a reference request. What is known about the following questions? Problem: Given a grammar $G$ (for example context-free) with language $L$ we can introduce a new grammar $G'$ which also ...
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### Counting sum of parities of cycle covers in cubic, planar, bipartite graphs

Let $G$ be a cubic (i.e. every degree exactly three), planar, bipartite graph. By Hall's theorem its edges can be partitioned into three perfect matchings. Take any such partition $M_0,M_1,M_2$ and ...
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### Optimal bounds for $k$-wise non-uniform random bits

Let $k\geq 2$ be a constant (in my case, $k=4$), and $n,t \geq 0$ be integers such that $2^t \leq n$. What is the smallest sample space (or, equivalent, how many true independent random bits are ...
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### Dequantumizability known and unknown?

Dequantumizable problems have been taking some headlines these days (for example https://www.scottaaronson.com/blog/?p=3880 and https://www.quantamagazine.org/teenager-finds-classical-alternative-to-...
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### 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 ...
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### Best algorithms for real linear programming

Linear Programming asks for $x\in\mathbb R^n$ such that $Ax\leq L$ holds where $A\in\mathbb R^{m\times n}$ and $L\in\mathbb R^m$ are given. Karmarkar has shown that $\ell$ is the number of bits of ...
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### Minimal generator for a set of sets

Is this a known problem? Given a set of sets $S$ find a set of sets $B$ s.t. each set in $S$ can be obtained through unions of some sets in $B$. The set $S$ is already a solution but the objective is ...
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### Hereditary Substitution with Inductives and Eliminators?

I'm wondering, is there any existing work on hereditary substitution with inductive type families and dependent eliminators? In particular, normalizing the application of an eliminator to an ...
203 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
359 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 ...
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### 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 ...
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### 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 ...
156 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
186 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $d$-...
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### 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 ...
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### 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 ...
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### 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 ...
287 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-...
311 views

### Max cut problem between two connected subgraphs

Let $G$ be a connected graph. Consider the problem of finding a partition $G = A \cup B$ into connected subgraphs, so that the cut between $A$ and $B$ is maximized. Is there anything which is known ...
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### Exact algorithm or parameterized algorithm for Maximum Edge Biclique Problem?

The Maximum Edge Biclique(MEB) problem is to find a biclique with as many edges as possible in a bipartite graph. It was proved to be NP-complete by Peeters in 2003, and then the inapproximability ...