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Questions tagged [reference-request]

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

219
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37answers
106k views

What Books Should Everyone Read?

[Timeline] This question has the same spirit of what papers should everyone read and what videos should everybody watch. It asks for remarkable books in different areas of theoretical computer ...
44
votes
4answers
3k views

Generalized Ladner's Theorem

Ladner's Theorem states that if P ≠ NP, then there is an infinite hierarchy of complexity classes strictly containing P and strictly contained in NP. The proof uses the completeness of SAT under many-...
109
votes
16answers
15k views

What Lecture Notes Should Everyone Read?

There has been several questions with the same scheme as this one: What papers should everyone read What books should everyone read What are the recent TCS books whose drafts are available online ...
63
votes
11answers
18k views

Uses of algebraic structures in theoretical computer science

I'm a software practitioner and I'm writing a survey on algebraic structures for personal research and am trying to produce examples of how these structures are used in theoretical computer science (...
555
votes
6answers
113k views

What's new in purely functional data structures since Okasaki?

Since Chris Okasaki's 1998 book "Purely functional data structures", I haven't seen too many new exciting purely functional data structures appear; I can name just a few: IntMap (also invented by ...
97
votes
37answers
13k views

What are the recent TCS books whose drafts are available online?

Following the post What Books Should Everyone Read, I noticed that there are recent books whose drafts are available online. For instance, the Approximation Algorithms entry of the above post cites ...
72
votes
20answers
7k views

Examples of “Unrelated” Mathematics Playing a Fundamental Role in TCS?

Please list examples where a theorem from mathematics which was not normally considered to apply in computer science was first used to prove a result in computer science. The best examples are those ...
31
votes
7answers
7k views

Books on programming language semantics

I've been reading Nielson & Nielson's "Semantics with Applications", and I really like the subject. I'd like to have one more book on programming language semantics -- but I really can get only ...
60
votes
17answers
3k 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 ...
39
votes
7answers
4k views

Truly random number generator: Turing computable?

I am seeking a definitive answer to whether or not generation of "truly random" numbers is Turing computable. I don't know how to phrase this precisely. This StackExchange question on "efficient ...
54
votes
2answers
3k views

Can one amplify P=NP beyond P=PH?

In Descriptive Complexity, Immerman has Corollary 7.23. The following conditions are equivalent: 1. P = NP. 2. Over finite, ordered structures, FO(LFP) = SO. This can be thought of as "...
24
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2answers
3k views
59
votes
14answers
11k views

Applications of topology to computer science

I'd like to write a survey on the applications of Topology in Computer Science. I plan to cover the history of topological ideas in Computer Science and also highlight a few current developments. It ...
32
votes
7answers
2k views

Algorithmic lens in the social sciences

Looking at questions through the algorithmic lens (i.e. from an algorithmic or complexity point of view) has become useful in disciplines outside of the 'standard domain' of computer science. In ...
19
votes
4answers
2k views

Computational complexity in quantitative finance

Predicting the stock market is hard! Can TCS make this sentiment more formal? Recently I have started thinking a little bit about finance, and was wondering how knowledge of TCS could help. Hedge ...
16
votes
2answers
908 views

A reading list on experimental algorithmics

As in, the area of the papers in the ACM Journal on Experimental Algorithmic JEA. Which were the foundational works? What are the main results? How are they characterized? Any interesting connections ...
16
votes
1answer
2k views

computing the minimal NFA for a DFA

Many years ago I heard that computing the minimal NFA (nondeterministic finite automaton) from a DFA (deterministic) was an open question, as opposed to the vice versa direction which has been known ...
26
votes
3answers
1k 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 ...
18
votes
3answers
589 views

Trade off between time and query complexity

Working directly with time complexity or circuit lower bounds is scary. Hence, we develop tools like query complexity (or decision-tree complexity) to get a handle on lower bounds. Since each query ...
14
votes
2answers
3k views

What is the “nearest” problem to the Collatz conjecture that has been successfully resolved?

I am interested in the "nearest" (and "most complex") problem to the Collatz conjecture that has been successfully solved (which Erdos famously said "mathematics is not yet ripe for such problems"). ...
8
votes
2answers
1k views

(0,1)-vector XOR problem

this is a rewrite of another recent question of mine [1] that wasnt stated well (it had a semi obvious simplification, mea culpa) but I think theres still a nontrivial question at the heart of it. ...
78
votes
41answers
15k views

Funny TCS-related papers etc?

What is the funniest TCS-related published work you know? Please include only those that are intended to be funny. Works which are explicitly crafted to be intelligently humorous (rather than, say, ...
32
votes
11answers
21k 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.
38
votes
1answer
2k views

Prerequisite for learning GCT

It seems that Geometric Complexity Theory requires much knowledge of pure maths such as algebraic geometry, representation theory. While I am a CS student and do NOT have classes of very abstract ...
43
votes
5answers
2k views

Historical reasons for adoption of Turing Machine as primary model of computation.

It's my understanding that Turing's model has come to be the "standard" when describing computation. I'm interested to know why this is the case -- that is, why has the TM model become more widely-...
25
votes
5answers
2k views

Subexponentially solvable hard graph problems

In light of the recent result of Arora, Barak, and Steurer, Subexponential Algorithms for Unique Games and Related Problems, I'm interested in graph problems that have subexponential time algorithms ...
17
votes
3answers
759 views

Formal Semantics of Programming Languages

I'm new to programming languages theory and I'm seeking for a good resource on a resource for formal semantics of programming languages. Specifically looking for structural operational semantics. I ...
28
votes
2answers
941 views

Kolmogorov's conjecture that $P$ has linear-size circuits

In his book, Boolean Function Complexity, Stasys Jukna mentions (page 564) that Kolmogorov believed that every language in P has circuits of linear size. No reference is mentioned and I couldn't find ...
14
votes
1answer
350 views

Lower bounds on the size of CFGs for specific finite languages

Consider the following natural question: Given a finite language $L$, what is the smallest context-free grammar generating $L$? We can make the question more interesting by specifying a sequence of ...
14
votes
1answer
577 views

Reading up on $BQP = BPP^{BQNC}$

What should I read to understand this problem? The power of small-depth quantum circuits. Is $BQP = BPP^{BQNC}$? In other words, can the "quantum" part of any quantum algorithm be compressed ...
6
votes
0answers
756 views

k-CNF ←→ k-DNF conversion to minimize errors

the following problem/question seems fundamental/hard. it appears in some circuit theory proofs, graph theory, and maybe elsewhere. looking for any nontrivial insight. will add various known/nearby ...
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 ...
2
votes
1answer
499 views

techniques or examples of analyzing a series of graphs

Let there be a sequence of graphs $G_1, G_2, G_3, ...$ constructed using some particular approach or algorithm. in this particular case $G_n$ is constructed by modifying $G_{n-1}$ in some "systematic" ...
2
votes
0answers
528 views

State of the art for SAT solvers [duplicate]

Possible Duplicate: Best Upper Bounds on SAT I'm working on the obstruction-set-free grid coloring problem; a specific instance of it is described in this previous question on coloring 17x17 ...
108
votes
17answers
7k views

Examples of the price of abstraction?

Theoretical computer science has provided some examples of "the price of abstraction." The two most prominent are for Gaussian elimination and sorting. Namely: It is known that Gaussian elimination ...
40
votes
6answers
2k views

Which model of computation is “the best”?

In 1937 Turing described a Turing machine. Since then many models of computation have been decribed in attempt to find a model which is like a real computer but still simple enough to design and ...
63
votes
11answers
3k 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}...
39
votes
18answers
4k views

What hierarchies and/or hierarchy theorems do you know?

I am currently writing a survey on hierarchy theorems on TCS. Searching for related papers I noticed that hierarchy is a fundamendal concept not only in TCS and mathematics, but in numerous sciences, ...
24
votes
4answers
2k views

Starting SAT solver papers

I want to make a first SAT solver. I know the SAT competition and the SAT conference, and there are just so many papers on this subject. I'm a starter, an overwhelmed starter. Where should I begin? ...
27
votes
5answers
2k views

Ecology and evolution through the algorithmic lens

The study of ecology and evolution is becoming increasingly more mathematical, but most of the theoretical tools seem to be coming from physics. However, in many cases the problems have a very ...
39
votes
3answers
3k views

Is the integer factorization problem harder than RSA factorization: $n = pq$?

This is a cross-post from math.stackexchange. Let FACT denote the integer factoring problem: given $n \in \mathbb{N},$ find primes $p_i \in \mathbb{N},$ and integers $e_i \in \mathbb{N},$ such that $...
28
votes
6answers
2k views

Alternative proofs of Schwartz–Zippel lemma

I'm only aware of two proofs of Schwartz–Zippel lemma. The first (more common) proof is described in the wikipedia entry. The second proof was discovered by Dana Moshkovitz. Are there any other ...
26
votes
3answers
1k views

Succinct Problems in $\mathsf{P}$

The study of Succinct representation of graphs was initiated by Galperin and Wigderson in a paper from 1983, where they prove that for many simple problems like finding a triangle in a graph, the ...
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 ...
23
votes
3answers
836 views

What are the relationships between those hypotheses in Fine-Grained Complexity Theory?

Complexity theory, through such concepts as NP-completeness, distinguishes between computational problems that have relatively efficient solutions and those that are intractable. "Fine-grained" ...
20
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2answers
891 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 ...
18
votes
1answer
2k views

Bitcoin and preventing double spending in decentralized digital currencies

A recent approach to creating a decentralized online currency, called Bitcoin, has been generating some interest. The goal is to have a way to transfer currency without a central authority and without ...
15
votes
5answers
834 views

References for Modular Decomposition

What are good papers/books to better understand the power of Modular Decomposition and its properties? I'm particularly interested in algorithmic aspects of Modular Decomposition. I have heard that ...
15
votes
3answers
955 views

Sources for Algorithmic Evolutionary Game Theory

I use the title term in a very loose sense. There is a significant amount of work on evolutionary game theory, including its mathematical foundations. I was recommended "Evolutionary Games and ...
2
votes
2answers
2k views

Book recommendations for CompSci related math

Searching for good textbooks on math related to Computer Science I bought two german books yet, but found them not to be easily understandable and not suitable for self-study . German textbooks are ...