Questions tagged [reference-request]
Reference-request is used when the author needs to know about work related to the question.
1,509
questions
5
votes
0answers
139 views
Dequantumizability known and unknown?
Dequantumizable problems have been taking some headlines these days (for example this blog post by Scott Aaronson and this article in Quantum Magazine).
What are some problems that are currently ...
4
votes
1answer
76 views
Comparative communication complexity?
I was reading the book "Communication Complexity" by Kuschilevitz and Nisan and in Exercise 1.18 they introduce a variant of the normal vanilla 2-person deterministic communication ...
0
votes
0answers
34 views
Weak simulation of Clifford circuits
Quantum circuits composed by Clifford gates can be simulated by classical computation in polynomial time. More precisely, this simulation should be a weak simulation, i.e. it is possible to sample the ...
0
votes
0answers
59 views
Name for words without squared symbols
Is there a common name in combinatorics for words that do not have square of size 1 ? That is words such that no symbols appears twice in a row or, more formally, words not in $\bigcup_{s\in\Sigma} \...
0
votes
0answers
59 views
Is there a term for 'no-turn-back walk' in graph theory?
Let $G$ be a finite undirected graph. A walk in $G$ is a finite sequence $<v_1,e_1,v_2,e_2,\dots,v_{k-1},e_{k-1},v_k>$ where $v_j$'s are vertices in $G$, $e_j$'s are edges in $G$, and $e_j=v_jv_{...
6
votes
1answer
143 views
Reference for automatically deriving dynamic programming algorithms from recursive algorithms?
This is what I'm looking for. Take a recursive algorithm:
def fib(n):
if n == 0 or n == 1:
return n
else:
return fib(n-1) + fib(n-2)
and turn it into ...
2
votes
0answers
56 views
Summing over weighted paths optimally
Given an edge-weighted directed graph, how do you sum over all weighted paths between A and B while using the smallest number of multiplications?
Is there a name for this problem?
This comes up in ...
3
votes
1answer
151 views
What is known about (upper bounds on) the LP gap of the (symmetric) Travelling salesman in special instances?
What is known about the LP gap of (the natural Held-Karp relaxation of) the (symmetric) Travelling salesman in special instances?
I'm only aware of one special case where the extreme points are all ...
4
votes
0answers
113 views
Split a string of positive numbers into substrings with decreasing totals
Suppose we're given a string of $n$ positive numbers and asked to split it into the maximum number of substrings whose totals are decreasing. I have an $O(n)$ time DP algorithm, but is it already ...
38
votes
12answers
28k views
Books on automata theory for self-study
I need a finite automata theory book with lots of examples that I can use for self-study and to prepare for exams.
6
votes
1answer
278 views
Complexity of optimal elimination for a planar tensor network
Edit Dec 15 it's not obvious this problem is tractable when further restricting to trees, see cs.SE question
Suppose we need to sum out variables in a tensor network (a factor graph where each ...
0
votes
0answers
32 views
Using error-correcting codes in multi-player games
There is a connection between any two from error-correcting codes, interactive schemes, and PCP. For quantum works, I found papers such as JV15 & Ji15. And there are classical examples about 20 ...
1
vote
0answers
39 views
Cycle double covers of cubic graphs using only a few cycles
This is a reference request question. Let $G$ be an arbitrary cubic graph.
Is the problem of finding a cycle double cover $D$ of $G$ with minimum number of cycles in $D$ studied in the literature?
I ...
1
vote
0answers
26 views
Cycle decompositions of locally linear 4-regular graphs
(Preface)
We consider only finite, simple, undirected graphs here. An orientation of a graph $G$ is obtained by assigning some direction to each edge of $G$.
(Question starts)
A graph is locally ...
2
votes
0answers
49 views
Bin packing with non-additive load functions
I am looking for information on the bin packing problem, where the load of each bin is not the sum of items in the bin, but some other monotone set function. For example, suppose each item $i$ has ...
0
votes
2answers
160 views
Is there an efficient construction for a trilinear pairing that has been used in theory or practice
A trilinear pairing is defined a function $e:G_1^3 \rightarrow G_2$, such that it satisfies the property $e(k_1^a, k_2^b, k_3^c) = e(k_1,k_2,k_3)^{abc}$
In general I am trying to solve the following ...
1
vote
0answers
33 views
Is arrangement-type graph on cyclic $k$-permutations of $n$ already studied?
The arrangement graph $A_{n,k}$ is the graph whose vertices are $k$-permutations of an $n$-vertex set $X$ (say, $X=\mathbb{Z}_n$) and two $k$-permutations are adjacent if they differ in exactly one ...
2
votes
0answers
77 views
NP-hardness of Euclidean k-Median for k = 2
In the Euclidean $k$-median problem, we are given a set $C$ of clients in $\mathbb{R}^d$. The task is to open a set $F \subset \mathbb{R}^d$ of $k$ facilities such that the cost function $\Phi(F) = \...
2
votes
0answers
54 views
Are there any references for this theorem of Lercher?
Let $\Delta = \lambda x.(x)x$ and consider $\Omega = (\Delta)\Delta$. Then $\Omega$ is exactly the only $\lambda$-term of the form $(\lambda x.t)v$ such that $(\lambda x.t)v=t\{v\ /\ x\}$.
Does ...
56
votes
7answers
4k views
For which problems in P is it easier to verify the result than to find it?
For (search versions) of NP-complete problems, verifying a solution is clearly easier than finding it, since the verification can be done in polynomial time, while finding a witness takes (probably) ...
6
votes
4answers
224 views
Type theory and fixed points of datatypes
For the purposes of this question, say that a datatype is a type constructor with one type parameter (this is sometimes called a type operator).
In Haskell, we can define a fixed point ...
13
votes
2answers
590 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
0answers
71 views
Complexity of detecting general position in the plane?
What is the complexity of detecting whether a given set of points in the plane is in general position? This surely must have been studied, but a quick search turns up nothing. For concreteness, let'...
5
votes
2answers
464 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 ...
6
votes
2answers
132 views
Reference request for linear algebra over GF(2)
I have been looking for materials on the linear algebra over $GF(2)$ but so far I haven't found any substantial textbooks or notes on this subject. In fact in one of the notes I found the introduction ...
4
votes
1answer
212 views
The "electricity packing" problem
The question is inspired by this paper.
In a distant village, there are $n$ electricity consumers. Consumer $i$ has a power demand of $d_i$ watts. The total electricity supply is $s$ watts. If $s\geq \...
4
votes
1answer
105 views
A counter example for the set mean objective
Let $\mathcal{P} = \{P_1, \cdots,P_n\}$ be a family of finite point sets in $\mathbb{R}^d$, each having at most $m$ points. Consider the following objective function
\begin{align}
cost(\mathcal{P},c) =...
8
votes
1answer
116 views
Construction of arbitrary functions with exponential-size $MODp \circ MODq$ circuits
It is mentioned in multiple papers [1], [2] that $MODp \circ MODq$ circuits for two distinct primes $p, q$ can compute arbitrary functions in exponential size. However, [1] provides no citation for ...
3
votes
2answers
540 views
What is "distributed computing" as a field of computer science?
I think it's field that studies distributed systems as described at http://en.wikipedia.org/wiki/Distributed_computing. There are distributed systems such as clusters and grids on top of this field. ...
5
votes
2answers
1k views
Full names of C. K. Chow and C. N. Liu
Where can I find the full names of C. K. Chow and C. N. Liu, of the Chow-Liu tree fame?
https://en.wikipedia.org/wiki/Chow%E2%80%93Liu_tree
https://ieeexplore.ieee.org/document/1054142
8
votes
2answers
2k views
Applications of computer science in biology
Is there a survey or tutorial article which talks about application of theoretical computer science to emerging fields of applications of computer science in biology, bioinformatics and nanotechnology?...
7
votes
0answers
118 views
Are the non-lazy / non-weak semantics of the $\lambda$-calculus related to weak evaluation?
Vague question
The most common semantics of the call-by-name $\lambda$-calculus (Hyland/Wadsworth’s observational equivalence $\approx_\text{HNF}$ and Morris’s observational equivalence $\approx_\text{...
9
votes
0answers
80 views
Expressiveness of pushdown automata whose stack height sequence is unambiguous
I consider pushdown automata on an alphabet $\Sigma$, which are intuitively finite automata with a stack. Formally, a pushdown automaton $A = (Q, q_0, F, \Gamma, \Delta)$ is a finite set $Q$ of states,...
6
votes
1answer
202 views
Lower bound for the OR problem
Let us have booleans $x_1, \cdots, x_n$. Any algorithm that determines $\bigvee_1^n x_i$ with probability at least $2/3$ requires $\Omega(n)$ time. It is not too difficult to prove this, but the proof ...
11
votes
7answers
18k views
What is the best text of computation theory/theory of computation?
In University we used the Sipser text and while at the time I understood most of it, I forgot most of it as well, so it of course didn't leave all to great of an impression. I borrowed that book and ...
0
votes
0answers
37 views
Is there a primal-dual algorithm for the Tree Augmentation Problem or the Cactus Augmentation Problem?
The TAP problem and the CacAP problem can be seen as covering problems for the minimum cuts of a graph.
It seems like these problems would fall under the framework of network design problems (...
38
votes
2answers
2k views
Multiplying n polynomials of degree 1
The problem is to compute the polynomial $(a_1 x + b_1) \times \cdots \times (a_n x + b_n)$. Assume that all coefficients fit in a machine word, i.e. can be manipulated in unit time.
You can do $O(n \...
5
votes
1answer
121 views
Regular Expressions that converts into unambiguous automata
Brüggemann-Klein and Wood (1992) proved that a certain kind of regular expressions, that they call “Deterministic Regular expressions”, when converted into automata using the Glushkov's Construction, ...
2
votes
2answers
116 views
Status of certain problems in knot theory
I found it somewhat difficult to understand the status of certain problems from knot theory. Is it correct to say that it's been neither proved nor disproved that any of the following problems are NP-...
1
vote
0answers
56 views
Canonical tester for dense graphs: from tester to removal lemma?
A theorem of Goldreich and Trevisan [1] on property testing in the dense graph model states the following (docusing on the one-sided part):
Suppose there exists a one-sided testing graph algorithm ...
7
votes
2answers
144 views
Algebraic characterisation of star-free safety languages
It is known that star-free languages are definable by aperiodic syntactic monoids.
But is there any algebraic characterisation of star-free safety $\omega$-languages?
Edit: A language $L$ is safety if ...
0
votes
0answers
75 views
Large CLIQUE approximation
I am interested in algorithms to identify large cliques in graphs where the largest clique is a large fraction (definitely greater than half, perhaps as great as 4/5) of the total number of vertices.
...
3
votes
2answers
286 views
Entropy-like quantity
For $p\in[0,1]^{\mathbb{N}}$ and $\alpha\ge1$, define
$$ H_\alpha(p) = \sum_{i\in\mathbb{N}}p_i|\log(p_i)|^\alpha.
$$
When $\sum_i p_i=1$ and $\alpha=1$, $H_1(p)$ is just the Shannon entropy of the ...
3
votes
0answers
74 views
Exact FPT Algorithm for Continuous Euclidean $k$-Means
The continuous Euclidean $k$-means problem is defined as follows:
Given a set $X$ of $n$ points in $d$ dimensional Euclidean space $\mathbb{R}^{d}$. Given a parameter $k>0$, find a partitioning $P$ ...
0
votes
1answer
98 views
Diophantine equations with bounds on variables
Solving Diophantine equations is famously known to be undecidable. What about Diophantine equations to be solved over a finite domain? In particular, if I put an upper bound $k$ over the value of the ...
0
votes
0answers
59 views
EXPSPACE-complete problems involving numbers
This is a subset of this question. I'm looking for EXPSPACE-complete problems, for using in a reduction, which involve numbers in some ways, since my target problem involves numbers and linear ...
2
votes
1answer
93 views
Property testable in sublinear time in bounded degree graphs but not in general graphs
Is there some natural property that is testable in strongly sublinear time (i.e. $O(n^{1-\epsilon})$ for some $\epsilon > 0$) in bounded-degree graphs but not in general graphs? If not such ...
10
votes
1answer
510 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 $O(1)$, ...
0
votes
0answers
75 views
Low-Treewidth Sorting Networks
It was previously asked if there exist Boolean circuits of treewidth $O(\log n)$ that compute the majority function $\text{MAJ}_n$ on $n$ inputs. While a construction using online algorithms and the ...
1
vote
1answer
210 views
Is this a novel technique for determining whether or not two rotated rectangles collide?
I was trying to determine whether or not two rectangles rotated around their centers were colliding and randomly thought to try the following algorithm:
Rotate both rectangles by the negative rotation ...
