Questions tagged [reference-request]

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

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78 views

Entropy bounds on solutions to problems in BPP and other complexity classes based on entropy demands

Has anyone studied the asymptotics of problems in complexity classes like $BPP$? The thought came to me that if a problem in $BPP$ only requires $O(log(n))$ bits of entropy to solve then, intuitively, ...
5
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1answer
104 views

$NP$ completeness of Hamiltonicity of cubic polyhedral plane graphs with bounded face degree?

Let $\mathscr{C}_d$ be the class of cubic 3-connected simple plane graphs, with face degree bounded by $d$. Is there any $d$ such that Hamiltonian cycle is $NP$ complete on $\mathscr{C}_d$? If so, ...
3
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2answers
206 views

Extending Hindley-Milner to type mutable references

I have been trying to implement a programming language from scratch, and have gotten reasonably far. It reads just like Python, other than the fact that let is used ...
4
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0answers
143 views

Is there a standard name for this way of modifying graphs?

Let $G = (V, E)$ be an undirected graph. Let me take an edge $\{x, y\}$ (in blue in the drawing) such that $x$ and $y$ have other incident edges. Among the incident edges we choose one edge $e_x = \{...
3
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1answer
120 views

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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1answer
59 views

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 ...
2
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1answer
126 views

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 ...
3
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0answers
112 views

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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0answers
68 views

Where is the flaw in this proof that an LP solves TSP? [duplicate]

In this preprint on Arxiv, M. Diaby, M.H. Karwan, and L. Sun give a Linear Program which they claim solves the Traveling Salesman Problem. In contrast to their prior work, which was asked about here, ...
4
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1answer
164 views

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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0answers
79 views

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 ...
6
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1answer
182 views

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 ...
4
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0answers
129 views

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 ...
2
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1answer
108 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 ...
5
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1answer
157 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 ...
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0answers
148 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 ...
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0answers
188 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, ...
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1answer
82 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 ...
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0answers
40 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 ...
4
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1answer
403 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 ...
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0answers
48 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. ...
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0answers
57 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 ...
10
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2answers
315 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 ...
6
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1answer
181 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 ...
2
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1answer
420 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 ...
5
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0answers
145 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
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1answer
145 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
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2answers
313 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 \...
10
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1answer
436 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 ...
5
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1answer
190 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}/\...
8
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1answer
167 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 ...
4
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3answers
178 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 ...
3
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2answers
137 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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1answer
68 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 ...
16
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0answers
426 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 ...
9
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2answers
172 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
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1answer
275 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\...
5
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3answers
453 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 ...
3
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1answer
130 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
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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
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0answers
71 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 ...
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0answers
35 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
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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 ...
13
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0answers
263 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-...
5
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2answers
168 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 ...
5
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1answer
111 views

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 ...
9
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0answers
101 views

Expected value of the evaluation of Boolean circuits of depth $2n$

I am not an expert on circuits and I wonder whether the following problem was already studied (and possibly solved). Any reference or suitable method to solve this question would be welcome. Let $C_{...
8
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1answer
129 views

Another planar separator ref question

Do any of you know a reference for the following (surprisingly tedious to prove) result? Given a connected planar graph $G$ with $n$ vertices and $n+t$ edges, it has a vertex separator of size $O( \...
4
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1answer
218 views

Fast algorithm to find a maximum connected subgraph of k vertices

Given an undirected graph $G = (V, E)$ and a function $f: 2^V \to \mathbb{R}^+,$ where $2^V$ is the set of all subsets of $V$. Find a connected subgraph $T = (V_T, E_T)$ of k vertices such that $f(V_T)...
3
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0answers
85 views

Critical Assignments vs Read-Once Branching Programs - Reference Request

Straight to the point: I'm looking for a reference for the fact that the complexity of a read-once branching program solving the search problem for an unsatisfiable formula $F$ is at least the ...