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Questions tagged [reference-request]

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

13
votes
1answer
278 views

Reference to lower bound on separator in a grid?

It is easy to verify that given the d dimensional grid of the integer points $\{1,\ldots,n\}^d$, with the regular adjacency, one can find a separator of size $n^{d-1}$ (just pick any middle hyperplane,...
7
votes
4answers
392 views

Complexity class separation in the presence of relativization barriers

Give an example of complexity classes $M$ and $N$ and oracles $A$ and $B$ such that 1. $M^A=N^A$ and 2. $M^B\neq N^B$ and 3. $M \neq N$.
29
votes
0answers
892 views

Does $EXP\neq ZPP$ imply sub-exponential simulation of BPP or NP?

By simulation I mean in the Impaglazzio-Widgerson [IW98] sense, i.e. sub-exponential deterministic simulation which appears correct i.o to every efficient adversary. I think this is a proof: if $EXP\...
4
votes
3answers
464 views

What applications of Cantor space are there?

Are there well-established applications of the Cantor space ($2^\omega$) in computer science, other than those connected with computable real arithmetic? John Tucker's page Computation on Topological ...
13
votes
2answers
902 views

Space alternating hierarchy

It is known thanks to Immerman and Szelepcsényi that ${\rm NSPACE}(f)={\rm coNSPACE}(f)$ if $f=\Omega(\log)$ (even for non-space constructible functions). In the same paper, Immerman state that the ...
12
votes
3answers
518 views

$NP\cap coAM$ Languages

What other problems languages different than graph isomorphism are in $NP\cap coAM$? Can you give some references? Update: I forgot to mention that I'm interested in languages not known to be in $...
18
votes
4answers
1k views

“All-different hypergraph coloring” - known problem?

I am interested in the following problem: Given a set X and subsets X_1, ..., X_n of X, find a coloring of the elements of X with k colors such that the elements in each X_i are all differently ...
27
votes
6answers
940 views

Well known classes of boolean formulas that require exponentially long resolution proofs

You might often find cutting plane methods, variable propagation, branch and bound, clause learning, intelligent backtracking or even handwoven human heuristics in SAT solvers. Yet for decades the ...
14
votes
5answers
2k views

History of recursion

Who introduced the idea of recursion? Can someone explain where it came from and how it impacted computer science?
20
votes
3answers
388 views

Property testing in other metrics?

There is a large literature on "property testing" -- the problem of making a small number of black box queries to a function $f\colon\{0,1\}^n \to R$ to distinguish between two cases: $f$ is a ...
37
votes
9answers
4k views

References for TCS proof techniques

Are there any references (online or in book form) that organize and discuss TCS theorems by proof technique? Garey and Johnson do this for the various kinds of widget constructions needed for NP-...
11
votes
1answer
238 views

Can someone suggest a recent survey on product form Markov chains?

I'm especially interested in their use in model checking applications. I have Open, Closed and Mixed Networks of Queues with Different Classes of Customers by Baskett et al. Any other suggestions ...
26
votes
3answers
2k views

Translating SAT to HornSAT

Is it possible to translate a boolean formula B into an equivalent conjunction of Horn clauses? The Wikipedia article about HornSAT seems to imply that it is, but I have not been able to chase down ...
25
votes
4answers
2k views

Bounded-cardinality bounded-frequency set cover: hardness of approximation

Consider the minimum set cover problem with the following restrictions: each set contains at most $k$ elements and each element of the universe occurs in at most $f$ sets. Example: the case $k = 4$ ...
25
votes
2answers
3k views
60
votes
17answers
4k views

Applications of TCS to classical mathematics?

We in TCS often use powerful results and ideas from classical mathematics (algebra, topology, analysis, geometry, etc.). What are some examples of when it has gone the other way around? Here ...
36
votes
5answers
1k views

Complexity of testing for a value versus computing a function

In general we know that the complexity of testing whether a function takes a particular value at a given input is easier than evaluating the function at that input. For example: Evaluating the ...
10
votes
5answers
3k views

What are good references on understanding online learning?

Specifically, I'm asking for resources to learn about machine learning systems that can update their respective belief networks (or equivalent) during operation. I've even run across a few, though I ...
17
votes
2answers
622 views

H-free cut problem

Suppose you are given a connected, simple, undirected graph H. The H-free cut problem is defined as follows: Given a simple, undirected graph G, is there a cut (partition of vertices into two ...
64
votes
11answers
4k views

What are good references to understanding the proof of the PCP theorem?

I'm familiar with a lot of results that use the PCP theorem (mainly in approximating algorithms), but I've never come across a clear explanation of the PCP theorem (ie, that $\mathsf{NP} = \mathsf{PCP}...
20
votes
2answers
926 views

Succinct circuit representation of graphs

The complexity class PPAD (e.g. computing various Nash equilibria) can be defined as the set of total search problems polytime reducible to END OF THE LINE: END OF THE LINE: Given circuits S and P ...
23
votes
3answers
945 views

Graph Isomorphism and hidden subgroups

I'm trying to understand the relationship between graph isomorphism and the hidden subgroup problem. Is there a good reference for this ?
21
votes
1answer
292 views

A comparison of extractors in terms of tradeoffs between time, randomness and space ?

Is there a good survey that compares different extractors, concentrators and superconcentrators and lays out the best methods in terms of the tradeoff between randomness, time and space ?
17
votes
3answers
732 views

Are there any known implementations for quantum computing constructs?

Quantum Computation is an active area of research that aims to take advantage of quantum physics (e.g. quantum entanglement) to advance the efficiency capabilities of computers (does not alter the ...