# All Questions

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15 views

### Confusion over how to merge for Huffman Coding Algorithim [closed]

I don't understand why the node formed at the circled step $"2"$ wasn't merged with the node coded with $"1011"$.
359 views

### Can I show algebraically that this regular expression accepts all binary strings?

The task is to prove that (0+1)* and 0*(1.0*)* are equivalent. 1. http://rubular.com/r/K9Hp9tU6px 2. http://rubular.com/r/N8VpoEcch4 EDIT: Forgot that + was ambiguous here! I want to prove that the ...
854 views

### Knapsack with dependent profits (pairs of items)

I'm working on a problem which MAY be reduced to the following version of Knapsack: Suppose two items $e_i$ and $e_j$ have profit $p_i$ and $p_j$ respectively. However, if both items are present in ...
93 views

### Reference request: Depth- (or Breadth-) first search with hints?

Consider the standard s-t reachability problem of finding a path between nodes $s$ and $t$ in a directed graph $G$. A DFS or BFS could solve it. Would it be possible to pre-process the graph and ...
293 views

### What podcast should everybody listen to?

This list was inspired by the lists: What are the popular science books that inspire TCS? What Books Should Everyone Read? What papers should everyone read? What videos should everybody watch? I don'...
520 views

### Approximately sampling from convex polyhedrons with quantum computers

Quantum computers are very good for sampling distributions that we don't know how to sample using classical computers. For example if $f$ is a Boolean function (from $\{-1,1\}^n$ to $\{-1,1\}$) that ...
33 views

### Efficient algorithm for finding segregators in a directed acyclic graph

Given a directed acyclic graph $G=(V,E)$, we define a $(\alpha,\beta)$-segregator of $G$ to be a subset $S$ of $V$ of size $\alpha$ such that no vertex in $G\setminus S$ has more than $\beta$ ...
123 views

### Weakest model of computation that can typecheck?

What's the weakest (known) model of computation (or smallest language class) that can decide whether a simply-typed lambda calculus program type checks? What about an (explicitly typed) CoC program?
57 views

### Approximation Ratio of Local search for $k-$center problem

In the $k-$center problem, you're given $V$ points in Eucledian space, and you're asked to get a subset $C\subset V, |C|=k$ such that $\max _{v\in V}d(v, Closest-Center(C,v))$ is minimized. Now I am ...
137 views

### 2DFA to 1DFA - Converting two way deterministic finite automata to one way deterministic finite automata

How can I convert a 2DFA to a normal DFA. Is there an algorithm/elegant way to do that ? I've been researching this for a few days but I coundn't find anything. Actually I want to implement that in ...
83 views

I am trying to understand the argument in the proof of Lemmma 6.3 (page 18) of this paper https://arxiv.org/abs/1902.08179. Let me summarize the conceptual crux of the argument here using a slightly ...
8k views

### How is proving a context free language to be ambiguous undecidable?

I've read somewhere that a Turing machine cannot compute this and it's therefore undecidable but why? Why is it computationally impossible for a machine to generate the parse tree's and make a ...
140 views

### An optimal subspace projection problem

Suppose we have a $k$-dimensional subspace $V$ in $\mathbb{R}^n$ given by a basis $\{v_1,\cdots,v_k\in \mathbb{R}^n\}$, find an index set $I\subset [n]$ with $|I|=m$ where $k\le m\le n$, such that \...
75 views

62 views

### Uniformly sampling or counting connected graph partitions with any number of blocks

Question: Is it possible to uniformly sample in polynomial time from the set of all connected partitions of a graph? Or is there a JVV type argument that proves this to be NP-hard? To clarify: By a ...
239 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 ...
108 views

### Multimodal logic with quantification over modal operators

I take a multimodal logic to be a logic with multiple (potentially infinitely many) primitive modal operators. I am curious if anyone has studied a logic that allows one to quantify over the modal ...
625 views

### Is there a problem that is easy for cubic graphs but hard for graphs with maximum degree 3?

Cubic graphs are graphs where every vertex has degree 3. They have been extensively studied and I'm aware that several NP-hard problems remain NP-hard even restricted to subclasses of cubic graphs, ...
71 views

### Decidability of rank-k polymorphism vs. System F

There's a paper by Kfoury from 1992, "Type Reconstruction in Finite Rank Fragments of the Second-Order $\lambda$-Calculus", that proves that type inference for Curry-style rank-$k$ polymorphic lambda ...
7k views

### Best Upper Bounds on SAT

In another thread, Joe Fitzsimons asked about "the best current lower bounds on 3SAT." I'd like to go the other way: What's the best current upper bounds on 3SAT? In other words, what is the time ...
110 views

### Types as abstract interpretations

In Types as Abstract Interpretations, Cousot seems to propose a method to derive various type systems by succesive abstract interpretation of the denotational semantics of an untyped lambda-calculus. ...
5k views

### Is there any connection between the diamond norm and the distance of the associated states?

In quantum information theory, the distance between two quantum channels is often measured using the diamond norm. There are also a number of ways to measure distance between two quantum states, such ...
### Finding the size $k$ subset in a metric space that maximizes the min distance between elements
I have a metric space $(X,d)$ and I'd like to find a subset of size k of far away elements. We can cast this as the following optimization problem \$\max_{S \subseteq X, |S| = k} ( \min_{i \not = j, ...