Tagged Questions

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

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5
votes
2answers
106 views

How to judge the definition of computational complexity of reals is natural or suitable?

As we know, definition of computational complexity of algorithm is almost without controversy, but the definition of computational complexity of reals or the computation models over reals is not in ...
3
votes
1answer
40 views

Can real-time deterministic multicounter automata recognize the marked palindrome language?

Consider the marked palindrome language which is defined as MPAL=$\{ w\#w^r | w \in \{a,b\}^* \}$. It is easy to recognize MPAL using only a single stack. My question is whether MPAL can be ...
2
votes
0answers
66 views

Presburger Arithmetic Decision Procedures

What are good textbook references for Presburger Arithmetic decision procedures?
10
votes
1answer
271 views

Decide the existence of a string homomorphism

Consider the following problem: Given two strings x,y, decide whether there exists a string homomorphism f such that f(x)=y. It is easy to show that this problem is in $NP$. Are there other ...
1
vote
0answers
132 views

intuition that VP=?VNP is (not?) connected to P=?NP

recently there has been major progress into the VP=?VNP problem for algebraic circuits originated by Valiant, inspiring some optimistic outlook on its eventual or imminent resolution.[1] what is ...
7
votes
2answers
321 views

Looking for Literature Source for Following idea

I am quite certain that I am not the first to entertain the idea that I am going to present. However, it would be helpful if I can find any literature related to the idea. The idea is to construct a ...
4
votes
1answer
134 views

Explaining computer science algorithms/concepts/ideas using metaphors

Recently I found an interesting algorithm book entitled 'Explaining Algorithms Using Metaphors' (Google books) by Michal Forišek and Monika Steinová. "Good" metaphors help people understand and even ...
11
votes
2answers
421 views

Long-Standing Conjectures later trivially proved by an implication

I'd like to know if there have been conjectures that have long been unproven in TCS, that were later proven by an implication from another theorem, that may have been easier to prove.
5
votes
1answer
134 views

Pseudorandom generators indistinguishable by uniform deterministic adversaries

I've seen pseudorandom generators defined for nonuniform efficient adversaries, or uniform probabilistic efficient adversaries. (For example, a monograph Pseudorandomness by Vadhan (here's its draft ...
6
votes
1answer
106 views

Are there presentations of set theory in terms of lambda-calculus?

I am planning to implement in software a set theory language, based on a binary function, which in set theory is the so called adjunction operation: $f(x, y) = x \cup$ {y}. Therefore, a presentation ...
7
votes
3answers
168 views

How high are the higher types that appear in practice?

This is admittedly a rather naively put and vague question, and I'm not sure how much more specific I want or can make it, but I'll try. By "practice" I mean surely in actual programming practice (of ...
10
votes
3answers
334 views

EXPSPACE-complete problems

I am currently trying to find EXPSPACE-complete problems (mainly to find inspiration for a reduction), and I am surprised by the small number of results coming up. So far, I found these, and I have ...
0
votes
1answer
35 views

Reference request: Classical analog of quantum threshold theorem

For quantum circuits, once the gate error is below a threshold, the error probability of an entire computation can be driven exponentially small with polylog costs in time and space: ...
10
votes
2answers
229 views

What is the minimum over all distributions of unit vectors of the variance of the dot product of the vectors?

I am trying to find a distribution over $n$ random vectors, say $x_1,\ldots, x_n$, on the $k$-dimensional unit sphere (where $n > k$) that minimizes $\max_{i\neq j} \mathrm{Var}(x_i^T x_j)$ subject ...
2
votes
2answers
94 views

Graph-theoretic properties of the Wiener index

The Wiener index of a graph is the sum of the lengths of the shortest paths between all pairs of its vertices. Are there useful graph-theoretic properties of this index?
2
votes
1answer
63 views

Weighted furthest point voronoi diagrams

I found that Weighted nearest neighbor voronoi diagrams are widely studied and there are optimal algorithms for that. But I could not find anything on Weighted furthest point voronoi diagrams !! But ...
12
votes
1answer
286 views

Optimal randomized comparison sorting

So we all know the comparison-tree lower bound of $\lceil\log_2 n!\rceil$ on the worst-case number of comparisons made by a (deterministic) comparison sorting algorithm. It does not apply to ...
10
votes
2answers
256 views

Minimum Tree-width of circuit for MAJORITY

What is the minimum tree-width of a circuit over $\{\wedge,\vee,\neg\}$ for computing MAJ? Here MAJ $:\{0,1\}^n \rightarrow \{0,1\}$ outputs 1 iff at least half of its inputs are $1$. I care ...
0
votes
1answer
60 views

Talk for K-12 Students + General Audience Reference Request

I will be giving talks about general topics in CS, and want to hit on TCS as well. The talks will be given to K-12 schools, so not all of them will be seniors who may go to an undergraduate program at ...
8
votes
0answers
284 views

Is it possible to solve perfect matching in linear time

As we know matching can be solve in polynomial time. One classical and famous algorithm is designed by Karp and Hopcroft. Is it possible to solve perfect matching problem in linear time for given ...
9
votes
1answer
84 views

First order satisfiability that doesn't have finite models

We know from Church's theorem that determining first order satisfiability is undecidable in general, but there are several techniques we can use to determine first order satisfiability. The most ...
7
votes
2answers
154 views

Implementation of surreal numbers for games

There is a very nice construction by Conway of surreal numbers. They are "numbers" that contain both real numbers and ordinals, are totally ordered, and have all the properties of a field (except they ...
8
votes
0answers
82 views

References for de-amortization

I've been interested in looking into the area of de-amortization recently (i.e. finding data structures with matching worst-case and amortized running time bounds, or exhibiting lower bounds against ...
1
vote
0answers
92 views

Strong Dependence

I asked this question on MO, but no answer. I don't know if this definition has been already given. Suppose $X$ and $Y$ are two random variables over finite alphabets $\mathcal{X}$ and ...
5
votes
1answer
112 views

Ref question: K-nearest neighbours in a graph

Given an undirected graph $G$ with $n$ vertices, $m$ edges, and positive weights on the edges, I am interested in the problem of computing for each vertex the $k$ distinct vertices in $G$ that are ...
0
votes
0answers
133 views

Problems which are solvable using Linear Programming

Can anyone share a link to a good survey/book about the different problem types for which we have a linear programming based solution for, as well as the related techniques?
3
votes
0answers
114 views

Restricted-Input Automaton

In the classic setting, an automaton for a language $L$ is required to accept all words in $L$ and reject/get stuck on every word in $\Sigma^*\setminus L$. All of the related concepts are then ...
2
votes
0answers
67 views

efficient data structures for generalized tensor products

The usual tensor product of vectors is a matrix. There has been tons of research into efficiently storing and operating on matrices in computers. But we can generalize the tensor product quite a ...
11
votes
0answers
148 views

Lower bounds for the size of nondeterministic circuits

It is known that the minimum size of $U_2$-circuits computing the parity function exactly equals $3(n-1)$. The lower bound proof is based on the gate elimination method. Recently, I noticed that the ...
-1
votes
2answers
78 views

Arrangements of Objects

Suppose there are $n$ bins each having $k$ objects. Assume that capacity of each bin is also $k$. Now we want to rearrange the objects such that each bin contains $k$ objects but this time if $x,y$ ...
8
votes
1answer
354 views

Problem that is in P only if P!=NP

Are there any problems that are solvable in polynomial time only if P!=NP, and otherwise solvable in (say) $O(2^n)$ time? A simple example would be: If P!=NP, compute a primality test for a random ...
13
votes
1answer
459 views

The complexity of counting simple paths in a directed graph

Let $G$ be a digraph (not necessarily a DAG) and let $s,t \in V(G)$. What is the complexity of counting the number of simple $s-t$ paths in $G$. I would expect the problem to be #${\mathsf ...
7
votes
1answer
230 views
0
votes
0answers
126 views

proving speedup phenomenon does not apply to any open complexity class separations

Aaronson recently wrote a blog refuting the idea that there could be some "glitch" in the formulation of the P vs NP conjecture[1] which reminds me of this following question. the Blum speedup ...
1
vote
0answers
90 views

How to define deep learning? [closed]

Ive read some articles about deep learning but I found its hard to provide a clear definition of deep learning. For me its like an intelligent feature selection method. But it seems that its not ...
2
votes
0answers
64 views

Which paper to cite when referring to reservoir sampling *with replacement*?

As far as I can tell, the term "reservoir sampling" is commonly used to refer to sampling without replacement and references [1], [2], and [3] are cited while mentioning it. When referring to ...
7
votes
0answers
89 views

Computing the most likely winner in elections : intermediate case between Kemeny and Borda?

Given $n$ possible alternatives satisfying some unknown linear ordering, a multiset of pairwise votes, i.e., a matrix $M\in\mathbb{N}^{n\times n}$: $M_{i,j}$ counts the number of votes for which ...
5
votes
1answer
131 views

What language $L \in NCM$ has $\overline{L} \not \in NCM$?

$NCM$, the class of non-deterministic reversal-bounded counter machines, has a lot of interesting dependability and closure properties. It's known that, unlike the deterministic version, NCM is not ...
4
votes
0answers
83 views

extracting/ exploiting similarity of SAT instances by solver

suppose that two SAT formulas on different variables $F_1, F_2$ are given on the input that are known to be true and the problem is to build an algorithm that finds a solution to each. the formulas ...
6
votes
1answer
275 views

Describing state machines mathematically

The short paper "Computer Science and State Machines" by Leslie Lamport seems quite strange to me. On the one hand, I am surprised to see that an important hardware protocol called "two-phase ...
1
vote
0answers
131 views

Definition of Planar 3-SAT

What is the standard definition of Planar 3-SAT? I have seen a number of different definitions. What was the original paper that defined it and proved it to be NP-complete?
4
votes
1answer
259 views

Hardness of UNAMBIGUOUS-3DM

Let UNAMBIGUOUS-3DM be defined by analogy to UNAMBIGUOUS-SAT, i.e. as a promise problem version of three-dimensional matching where we may assume there is no more than one solution. Is there a ...
2
votes
1answer
95 views

Resource listing models with known VC dimension

Is there any reference resource gathering models with known VC dimension? I am looking for an exhaustive list of models with their VC dimension (and ideally the associated proof or a pointer to it). ...
13
votes
0answers
289 views

How can one find the “hard” probability distribution on the input for recursive boolean functions?

Update: Since, it seems there is no progress regarding this question, any idea, conjecture, hunch, or advice is welcome. For example, are there any partial or incomplete results? What are the main ...
3
votes
0answers
74 views

minimal languages that “cover” grammar productions

this question is based on generalizing two somewhat similar questions that recently appeared on the "sister" beta site cs.se (now with more questions than this one!) and which seems theoretically ...
0
votes
0answers
77 views

Graph database indexing

Graph databases are usually defined as index-free adjacency and that applies mostly to many current implementations - for example Neo4j - My question is: Is there are any references or papers with ...
6
votes
0answers
45 views

Explicit error bounds on the abelian hidden subgroup problem

What are some explicit forms for the error probability in the typical quantum abelian hidden subgroup algorithm as a function of oracles queries? Ettinger, Hoyer, and Knill give a result that the ...
19
votes
0answers
313 views

$RL=L$ Progress Since 2006

Reingold, Trevisan, and Vadhan's breakthrough 2006 paper (http://dl.acm.org/citation.cfm?id=1132583) reduced the problem of showing $RL=L$ to producing pseudorandom walks on regular digraphs that are ...
7
votes
0answers
157 views

Gaussian elimination for inverting matrices modulo prime power

Can I use Gaussian elimination to compute matrix inverse over the ring $\mathbb{Z}_{p^k}$ (ring of residues modulo $p^k$) where $p$ is prime and $k$ is an integer greater than $1$? Such matrix is ...
4
votes
1answer
90 views

any relation/ overlap between small world graphs, scale free graphs, and expander graphs?

small world graphs (eg Watts-Strogatz model & others) and scale free graphs are a relatively recently discovered graph type via mainly empirical analysis of large real-world graphs (eg via Big ...