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2
votes
1answer
47 views

Promise Variant of Set-Packing

An instance of the SET-PACKING problem is given by a list of sets $\mathcal{S} = \{S_1,\dots,S_m\} \subseteq 2^U$. It is a ``yes'' instance iff there exists some subset $\mathcal S'$ of $\mathcal S$ ...
3
votes
2answers
235 views

computing maximal bit density over a FSM

let $L$ be a regular language defined by a FSM over binary symbols $\{0,1\}$. consider a function $f(x)$ on words/ strings that computes "bit density", defined as the number of $1$'s in a word ...
1
vote
0answers
128 views

Looking for reference on NP-Completeness of proofs of length n

Given a deductive system $\Lambda$, and some well-formed-formula S, one can ask the question "Is there a proof S in $\Lambda$ of length n?" If n is presented in base-1 and if all the axioms of ...
10
votes
1answer
194 views

Hartmanis-Stearns conjecture and the computable transcendental numbers

In the 1965 article "On the computational complexity of algorithms" by Hartmanis and Stearns, the authors conjecture that if a real-time Turing Machine computes the real number $r$ in, for example, ...
2
votes
1answer
117 views

minimal finite automata given in-words and out-words

this seems an interesting FSM optimization problem; have not seen it studied, wondering if it has been and/ or looking for other insight. given: two finite sets of words $S_{in}$ and $S_{out}$. ...
2
votes
1answer
67 views

Lower bounds and impossibility results for distributed transactions

I am studying on distributed transactions, mainly on the correctness criteria (e.g., serializability (SR) and snapshot isolation (SI) in replicated settings) and their implementations. To avoid ...
7
votes
1answer
94 views

Extensional characterization of non-deterministic finite state transductions

I recently became aware of the rather appealing characterization of deterministic word-to-word transductions as word functions with bounded variation (see e.g. [1]). This coincides with the set of ...
13
votes
1answer
322 views

“Snake” reconfiguration problem

While writing a small post on the complexity of the videogames Nibbler and Snake; I found that they both can be modeled as reconfiguration problems on planar graphs; and it seems unlikely that such ...
10
votes
2answers
442 views

Lower bound on estimating $\sum_{k=1}^n a_k$ for non-increasing $(a_k)_k$

I'd like to know (related to this other question) if lower bounds were known for the following testing problem: one is given query access to a sequence of non-negative numbers $a_n \geq \dots\geq a_1$ ...
8
votes
1answer
163 views

What are the major research issues in distributed transactions?

Background: Transaction processing has been a traditional research topic in database theory. Nowadays distributed transactions are popularized by the large-scale distributed storage systems which ...
0
votes
2answers
105 views

Where can I find the proof of the theorem and what is the computational complexity of the computably isomorphic map?

"any two representations of reals which are acceptable are actually computably isomorphic",please see here for reference where may proof of this theorem be found, and what is the the computational ...
-2
votes
1answer
63 views

For two representations of finite length of one computable number are there $P$-time algorithms that compute one from another

Any computable number may have different representations of finite length . For example,$\sqrt{2}$ may be represented as root of equation, or as a (shortest for a universal Turing Machine)program of ...
0
votes
0answers
61 views

What are the differences between data partition and data replication regarding distributed transaction?

For a large-scale distributed database (or storage) system, data is often partitioned (wiki) (a.k.a sharding) and/or replicated (wiki) across different nodes. Roughly speaking, data partition splits ...
1
vote
1answer
120 views

Reference for unpublished but quoted manuscript

Is there a place to locate the reference "[Smi88] D. V. Smirnov, ``Shannon's Information Methods for Lower Bounds for Probabilistic Communication Complexity,'' Master's thesis, Moscow University, ...
8
votes
2answers
158 views

Understanding graph minor theorem

This question is two-fold, and is mainly reference-oriented: Is there somewhere where the main intuitions for proving graph minor theorem are given, without going too much into the details? I know ...
1
vote
0answers
82 views

What is the name of this data structure? (hash table with a limit on the number of entries)

Denote $[n] \triangleq \{1,2,\ldots,n\}$. Assume we would like to have a data structure $S$ which kinda works as a dictionary from $[k]$ to $[v]$, and supports add/remove/update/query functionality, ...
8
votes
2answers
233 views

Enumerating Planar Graphs of Bounded Treewidth

I am looking for references for the following problem: given integers $n$ and $k$, enumerate all non-isomorphic planar graphs on $n$ vertices and treewidth $\leq k$. I'm interested both in theoretical ...
4
votes
2answers
177 views

Flat vs non-flat domains

My understanding is that, more often than not, when people use domain theory for higher-type computability or the denotational semantics of functional programming languages, they tend to prefer flat ...
4
votes
1answer
155 views

Is it decidable that a computable analytic function over $\mathbb{R,C} ,$ equals $0$

Is it decidable whether a computable analytic function $f(x_1,x_2,\dots,x_n)$ over $\mathbb{R}$, $\mathbb{C}$ in a semi-algebraic or semi-analytic domain is identically zero? Is there any algorithm? ...
10
votes
2answers
223 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 ...
5
votes
2answers
104 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 ...
3
votes
0answers
81 views

Presburger Arithmetic Decision Procedures

What are good textbook references for Presburger Arithmetic decision procedures?
10
votes
1answer
533 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
162 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 ...
8
votes
2answers
355 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 ...
7
votes
4answers
309 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 ...
13
votes
2answers
494 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.
6
votes
1answer
170 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
154 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
214 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 ...
12
votes
3answers
569 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
42 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
241 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
104 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
75 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
301 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
278 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
70 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
300 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
120 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
184 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 ...
9
votes
0answers
99 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 ...
2
votes
0answers
113 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 ...
7
votes
1answer
197 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
150 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
129 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
91 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 ...
16
votes
1answer
269 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
79 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 $x,y$ ...
9
votes
1answer
372 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 ...