List of unsolved problems in computer science

http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_computer_science

by jonbaer • 13 years ago

99 40 13 years ago

en.wikipedia.org

sauravt• 13 years ago

List of unsolved problem in Mathematics http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_ma...

MojoJolo2• 13 years ago

What is the fastest algorithm for multiplication of two n-digit numbers?

What is the fastest algorithm for matrix multiplication?

I think those "What is the fastest" questions are relative. In my opinion, they are not unsolved problem. There are already solutions for them. And in those current solutions, there is of course the fastest.

When a faster algorithm is formulated, a time will come where another algorithm will perform much better.

EDIT: Now I get it. That "fastest" is in terms of time complexity. Thanks guys. :)

ginko2• 13 years ago

I believe fastest in this context means that it has been proven that there can be no faster algorithm.

MojoJolo2• 13 years ago

Is it really possible? I believe the "fastness" of something is infinite because of numbers being endless.

wlievens• 13 years ago

Indeed, in terms of complexity theory I would guess, not in terms of milliseconds.

fractalsea2• 13 years ago

With regards to matrix multiplication[1]:

I think the hidden subtext here is that many people believe there exists a O(n^2) algorithm for matrix multiplication, but it has not been discovered yet.

[1] Wouldn't be surprised if this is the case for the other problem too, although I don't know much about it.

amund• 13 years ago

Ran Raz proved that Matrix Inversion is O(n^2 lg n), ref: Ran Raz. On the Complexity of Matrix Product. SIAM Journal on Computing, 32(5):1356–1369, 2003.

Based on that I deduced that Matrix Multiplication is O(n^2 lg n), http://amundtveit.info/publications/2003/ComplexityOfMatrixI...

Regarding even faster operations, it has been hypothetized that all matrices are Toeplitz or Hankel (which have O(n lg n) algorithms), ref: D. S. Mackey, N. Mackey, and S. Petrovic. Is Every Matrix Similar to a Toeplitz Matrix. Linear Algebra & its Applications, 297:87105, 1999. But that was proved to not be the case: T. Amdeberhan and G. Heinig - http://www-math.mit.edu/~tewodros/georgmemoriam.pdf

jd0072• 13 years ago

It's talking about big O time complexity, which means you have to prove that there can be no faster algorithm. For example comparison sort (so no radix) can be no faster than O(nlogn).

fractalsea2• 13 years ago

It would be nice to see more. I'm sure there are.

Having said that I suppose most problems we face in this field boil down to mathematical problems at the fundamental level. At least that's the conclusion I came to when I tried to think of unsolved AI problems.

k__• 13 years ago

I like how the POPLmark sounds like popel-mark in german. Which would mean something like booger-money in english.

gbog6• 13 years ago

I'd like to see some more general unsolved problems concerning big code bases, programming languages, etc. Examples:

- Object-relational impedance mismatch

- MVC (solves only half of the problem)

- Global state

- Schema vs schemaless data stores

- Raising exceptions vs returning error codes

A good sign of an unsolved problem in this regard is that programmers go back and forth between solutions, forgetting the downsides of the previous flavour while enduring the downsides of the current flavour.

Very often, one new solution pretends it will get rid of complexity, but the actual complexity is just moved a bit further behind the carpet.

dbaupp• 13 years ago

Genuine question: wouldn't those be better suited to a "Unsolved problems in software engineering" list?

gbog6• 13 years ago

Yes.

chongli5• 13 years ago

>Object-relational impedance mismatch

This one is easy: don't do it! If you're talking to a database, you should be using a powerful and declarative language for building your queries.

>Global state

This is a solved problem from a computer science perspective. The rest of the work is getting programmers to understand how and change their habits accordingly.

>Raising exceptions vs returning error codes

Option/Either types are a very strong middle ground. They don't require the boilerplate of checking error codes and they don't have the unpredictability of exceptions (particularly in the case of asynchronous code).

>Very often, one new solution pretends it will get rid of complexity, but the actual complexity is just moved a bit further behind the carpet.

I know what you mean. A lot of solutions end up "punting" the complexity to some other structure. The real answer (if there can be one) is to find ways to eliminate this complexity altogether. One major way to do that is to work with values and compose pure functions to build them. Pure functions dramatically improve one's ability to reason about their properties in isolation.

gbog6• 13 years ago

About global state: yes global state can be avoided most of the time, but the fact that there is still some pressure to use it show it is not that obvious, or, said otherwise, that no other solution is able to cover all use cases.

For example, GOTO is bad and has gone for good and I have never heard of some coders missing it (except for the fun), so it is a solved problem. But if you need to dynamically set a value and use it in a very remote part of the code, the need for some global state arise and is hard to avoid.

About ORM: sure, but these still exists and are widespread, so the solution must be not that obvious.

About complexity: yes also, but I think a really efficient way to properly "dissolve" complexity (and not push it somewhere lese) is to have good data structures.

tel4• 13 years ago

I want to elaborate on "values" since I've been thinking about them all morning. They're just a simplification of all of programming.

Everyone remembers the first time that they learned how messy IEEE Floating Point math actually is. You were probably trying to treat Floats like R and then the abstraction leaked all over you. The same thing happens with int32/64 types when they roll over on you or (worse) throw exceptions. There's a mismatch between your mental model of these objects and their actual behavior. Anyone who's ever used BigInts has probably noticed the sigh of relief you get when you make that tradeoff: "these might be arbitrarily slow, but I also know that my computations will work exactly how I expect pretty much forever".

(Yes, you can flat out overflow your memory if you want, but even if it has to swap to your disk for 30 years, the value is intact.)

That sigh of relief is the thing we should be buying with our massive CPUs.

That's also exactly the premise of immutable values. They get computed and then they stay computed allowing you to have an extremely low-impact mental model of their behavior. They work platonically—once you compute them they just exist to be inspected.

Better than that, values you compute can often be finite or efficiently infinite structures so that you don't even truly worry about arbitrary slowdowns. It's relatively easy to play within the "easily computable" playground.

Nobody—not even the purest Haskeller—thinks that everything ought to have value semantics. Instead, they just form a significantly simpler underlying language. This just leaves less room for the semantics of your language to be complicated. They only get complicated when you legitimately want them to—so if you want mutable skiplists then you can have them by creating an environment where values has mutable properties. And then that environment, ST, is itself a value that you can pass around. (That's half the point of Monads.)

v13inc• 13 years ago

"""This one is easy: don't do it! If you're talking to a database, you should be using a powerful and declarative language for building your queries."""

Not only that, but I have been finding that most problems where I would originally turn to using objects and classes are better solved by using static functions that operate on large data structures. This strategy also helps sidestep the object-relational mismatch in a lot of cases.

dsego• 13 years ago

- Object-relational impedance mismatch

See the Third Manifesto for a possible solution http://www.thethirdmanifesto.com

miguelrochefort• 13 years ago

Don't forget Knowledge Representation problems.

_pmf_• 13 years ago

> - Raising exceptions vs returning error codes

Common Lisp actually defines a third variant (condition/restart).

I would add the following (which have all been done in some languages, of course):

* composable abstractions

* modules at the language level, i.e. making ad-hoc dependency injection (whether manually of framework driven) obsolete

gcr2• 13 years ago

This article is about unsolved questions in computer science philosophy, not computer engineering practice.

shawnz• 13 years ago

You seem to be talking about a different kind of "problem" than the article. What you list are patterns that have advantages and disadvantages, where the "solution quality" is a matter of opinion. The article talks about things which haven't been proven yet.

larsberg• 13 years ago

POPLmark seems to generally be considered solved. There are multiple good solutions using different tools for all of those problems, I believe.

And the real goal has largely been reached. At this point, if you're proposing new PL theory and you don't have a mechanised proof of it, the entire work is viewed with considerable skepticism.

That said, reuse and productivity are still not much better than that of real-world software. My peers who do that sort of thing are in very high demand for post-doc positions on projects funded by various governments/militaries to "prove the X property about software system Y."

gerhardi• 13 years ago

How about a list of greatest problems in computer science that have been solved? Would make a nice list to study and to gain general knowledge!

aaron695• 13 years ago

I don't know, I consider them more unsolved mathematics problems in the non academic world.

I know tomato tomato, but to me in computer science it's more important to know if they have been solved for most cases (Or alternatively considered probably to hard in RL)

Getting to caught up in perfect solutions can be more a hindrance.

tel4• 13 years ago

I'm going to bicker about language, but that sounds more like a software engineering mindset. Most of the most fundamental problems in computer science have exactly that kind of mathematical nature.

Works well enough gets a paycheck, but doesn't impact the field.

gcr2• 13 years ago

The name you're looking for is "Unsolved problems in computer engineering." I agree; there should be an article for that, but it should be kept separate from this one.

List of unsolved problems in computer science

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