All Questions
12,593
questions
616
votes
6
answers
130k
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 ...
- 8,861
483
votes
72
answers
181k
views
What papers should everyone read?
This question is (inspired by)/(shamefully stolen from) a similar question at MathOverflow, but I expect the answers here will be quite different.
We all have favorite papers in our own respective ...
380
votes
92
answers
114k
views
Algorithms from the Book
Paul Erdős talked about the "Book" where God keeps the most elegant proof of each mathematical theorem. This even inspired a book (which I believe is now in its 4th edition): Proofs from the ...
327
votes
29
answers
202k
views
Core algorithms deployed
To demonstrate the importance of algorithms (e.g. to students and professors who don't do theory or are even from entirely different fields) it is sometimes useful to have ready at hand a list of ...
- 7,609
268
votes
39
answers
142k
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 ...
259
votes
11
answers
99k
views
What is the enlightenment I'm supposed to attain after studying finite automata?
I've been revising Theory of Computation for fun and this question has been nagging me for a while (funny never thought of it when I learnt Automata Theory in my undergrad). So "why" exactly do we ...
- 5,255
230
votes
60
answers
97k
views
Major unsolved problems in theoretical computer science?
Wikipedia only lists two problems under "unsolved problems in computer science":
P = NP?
The existence of one-way functions
What are other major problems that should be added to this list?
Rules:
...
230
votes
11
answers
121k
views
Is Norbert Blum's 2017 proof that $P \ne NP$ correct?
Norbert Blum recently posted a 38-page proof that $P \ne NP$. Is it correct?
Also on topic: where else (on the internet) is its correctness being discussed?
Note: the focus of this question text has ...
- 1,669
154
votes
39
answers
47k
views
What videos should everybody watch?
Stanford University now has a Youtube channel, with free access to HD video of full courses on everything from dynamical systems to quantum entanglement. More conferences and workshops are ...
145
votes
2
answers
19k
views
Super Mario Galaxy problem
Suppose Mario is walking on the surface of a planet. If he starts walking from a known location, in a fixed direction, for a predetermined distance, how quickly can we determine where he will stop?
...
- 23k
141
votes
30
answers
25k
views
Problems Between P and NPC
Factoring and graph isomorphism are problems in NP that are not known to be in P nor to be NP-Complete. What are some other (sufficiently different) natural problems that share this property? ...
128
votes
11
answers
12k
views
How hard is unshuffling a string?
A shuffle of two strings is formed by interspersing the characters into a new string, keeping the characters of each string in order. For example, MISSISSIPPI is a ...
- 23k
123
votes
13
answers
13k
views
Advice on good research practices
After reading Daniel Apon's question, I started thinking that it might be useful (especially to junior researchers and graduate students like me) to ask a broader and more general question so we can ...
123
votes
18
answers
9k
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 ...
122
votes
15
answers
19k
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
...
113
votes
7
answers
10k
views
Solid applications of category theory in TCS?
I've been learning a few bits of category theory. It certainly is a different way of looking at things. (Very rough summary for those who haven't seen it: category theory gives ways of expressing all ...
- 27.1k
106
votes
6
answers
53k
views
How do the state-of-the-art pathfinding algorithms for changing graphs (D*, D*-Lite, LPA*, etc) differ?
A lot of pathfinding algorithms have been developed in recent years which can calculate the best path in response to graph changes much faster than A* - what are they, and how do they differ? Are ...
105
votes
5
answers
24k
views
List of TCS conferences and workshops
I would like to ask for help in compiling a list of as many TCS-related conferences and workshops as possible. My main motivation for doing this is to plan possible blog coverage of more theory ...
102
votes
39
answers
15k
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 ...
102
votes
15
answers
11k
views
A simple decision problem whose decidability is not known
I am preparing for a talk aimed at undergraduate math majors, and as part of it, I am considering discussing the concept of decidability. I want to give an example of a problem that we do not ...
- 11.9k
95
votes
9
answers
19k
views
What would it mean to disprove Church-Turing thesis?
Sorry for the catchy title. I want to understand, what should one have to do to disprove the Church-Turing thesis? Somewhere I read it's mathematically impossible to do it! Why?
Turing, Rosser etc ...
user200
94
votes
7
answers
30k
views
What is the contribution of lambda calculus to the field of theory of computation?
I'm just reading up on lambda calculus to "get to know it". I see it as an alternate form of computation as opposed to the Turing Machine. It's an interesting way of doing things with functions/...
- 5,255
94
votes
2
answers
40k
views
What is the actual time complexity of Gaussian elimination?
In an answer to an earlier question, I mentioned the common but false belief that “Gaussian” elimination runs in $O(n^3)$ time. While it is obvious that the algorithm uses $O(n^3)$ arithmetic ...
- 23k
93
votes
14
answers
21k
views
What kind of mathematical background is needed for complexity theory?
I am currently an undergraduate student, bound to graduate this year. After graduation, I am considering to work towards a TCS master/PhD. I have begun wondering what fields of mathematics are ...
- 3,751
88
votes
2
answers
12k
views
Was the reduction in Shor's algorithm originally discovered by Shor?
This is a "historical question" more than it is a research question, but was the classical reduction to order-finding in Shor's algorithm for factorization initially discovered by Peter Shor, or was ...
user1338
85
votes
20
answers
11k
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 ...
84
votes
42
answers
17k
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, ...
84
votes
9
answers
10k
views
Are research papers hard to read?
This question may not suit to here, but I couldn't find a better place to ask (it was closed in SO).
I find research papers on computer science hard to understand. Of course the subjects are ...
- 959
83
votes
5
answers
4k
views
Techniques for Reversing the Order of Quantifiers
It is well-known that in general, the order of universal and existential quantifiers cannot be reversed. In other words, for a general logical formula $\phi(\cdot,\cdot)$,
$(\forall x)(\exists y) \...
- 16.4k
80
votes
8
answers
44k
views
What would a very simple quantum program look like?
In light of the announcement of the world's first programmable quantum photonic chip, I was wondering just what software for a computer that uses quantum entanglement would be like. One of the first ...
- 921
79
votes
14
answers
23k
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 (...
- 893
75
votes
9
answers
16k
views
Powerful Algorithms too complex to implement
What are some algorithms of legitimate utility that are simply too complex to implement?
Let me be clear: I'm not looking for algorithms like the current asymptotic optimal matrix multiplication ...
74
votes
4
answers
39k
views
Why is 2SAT in P?
I've come across the polynomial algorithm that solves 2SAT. I've found it boggling that 2SAT is in P where all (or many others) of the SAT instances are NP-Complete. What makes this problem different? ...
- 1,195
73
votes
9
answers
11k
views
Are runtime bounds in P decidable? (answer: no)
The question asked is whether the following question is decidable:
Problem Given an integer $k$ and Turing machine $M$ promised to be in P, is the runtime of $M$ ${O}(n^k)$ with respect to input ...
- 1,506
72
votes
12
answers
9k
views
How important is knowing how to program for TCS?
Coming from a more mathematical background, I never really learned how to code.
I am starting a PhD in TCS and many people were surprised by how little I knew about programming (and about computer in ...
- 1,655
72
votes
14
answers
19k
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 ...
- 841
71
votes
17
answers
9k
views
Polynomial-time algorithms with huge exponent/constant
Do you know sensible algorithms that run in polynomial time in (Input length + Output length), but whose asymptotic running time in the same measure has a really huge exponent/constant (at least, ...
71
votes
13
answers
9k
views
Common false beliefs in theoretical computer science
This post is inspired by the one in MO: Examples of common false beliefs in mathematics.
Since the site is designed for answering research level questions, examples like $\mathsf{NP}$ stands for non-...
70
votes
7
answers
4k
views
Which interesting theorems in TCS rely on the Axiom of Choice? (Or alternatively, the Axiom of Determinacy?)
Mathematicians sometimes worry about the Axiom of Choice (AC) and Axiom of Determinancy (AD).
Axiom of Choice: Given any collection ${\cal C}$ of nonempty sets, there is a function $f$ that, given a ...
- 27.1k
69
votes
10
answers
9k
views
Are there any open problems left about DFAs?
After studying deterministic finite state automata (DFA) in undergrad, I felt they are extremely well understood. My question is whether there is something we still don't understand about them. I don'...
- 612
68
votes
17
answers
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 ...
68
votes
5
answers
6k
views
The origin of the notion of treewidth
My question today is (as usual) a bit silly; but I would request you to kindly consider it.
I wanted to know about the genesis and/or motivation behind the treewidth concept. I sure understand that ...
- 1,953
68
votes
7
answers
4k
views
Are $PSPACE$-complete problems inherently less tractable than $NP$-complete problems?
Currently, solving either a $NP$-complete problem or a $PSPACE$-complete problem is infeasible in the general case for large inputs. However, both are solvable in exponential time and polynomial space....
- 4,670
67
votes
3
answers
9k
views
How do I referee a paper?
Updated below
We all know the critical importance of peer-review. It is the main form of quality control and feedback on research. However, to an early-stage researcher (like me), it can sometimes ...
67
votes
3
answers
7k
views
Why does Fourier analysis of Boolean functions "work"?
Over the years I have gotten used to seeing many TCS theorems proved using discrete Fourier analysis. The Walsh-Fourier (Hadamard) transform is useful in virtually every subfield of TCS, including ...
user887
65
votes
11
answers
5k
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}...
- 1,459
65
votes
10
answers
12k
views
One Stack, Two Queues
background
Several years ago, when I was an undergraduate, we were given a homework on amortized analysis. I was unable to solve one of the problems. I had asked it in comp.theory, but no ...
- 16.4k
65
votes
5
answers
2k
views
Problems that can be used to show polynomial-time hardness results
When designing an algorithm for a new problem, if I can't find a polynomial time algorithm after a while, I might try to prove it is NP-hard instead. If I succeed, I've explained why I couldn't find ...
- 13.5k
65
votes
1
answer
3k
views
More on PH in PP?
A recent question by Huck Bennett asking whether the class PH was contained in the class PP, received somewhat contradictory answers (all true, it seems). On one hand, several oracle results were ...
- 9,359
63
votes
12
answers
3k
views
Parameterized complexity from P to NP-hard and back again
I'm looking for examples of problems parametrized by a number $k \in \mathbb{N}$, where the problem's hardness is non-monotonic in $k$. Most problems (in my experience) have a single phase transition, ...
- 2,799