Complexity Definition and 129 Threads

I'm not entirely clear on the concept of kolmogorov complexity. Does it mean that the a certain string is complex if there is no combinatorial (not sequential) circuit which outputs that string or does it mean that a certain string is complex if there is no program which can output that string...

Hi everyone! I have a question for you :) I am wondering, if there already is a developed model, imitating insect wings, e.g. bee wings. If you happen to observe them, they seem to be much more complex, but also much more useful and allow a more flexible movement. Insects fly with them not...

Let's say I have some algorithm with complexity O(n^k) for some constant k. and let's say it runs in some time T. Now, I want to implement a divide and conquer approach for this algorithm, by dividing the problem in half each recursion. So basically, the first time i run my algorithm it will run...

Besides being a partially ordered set by set inclusion, what else is the set of all classes O(f) where f:N->N.

I'm sure there are lots of way to define complexity in different contexts. Some that I've heard of include: -Minimum description length / Kolmogorov complexity -time complexity - number of steps to compute -parameter complexity - number of parameters needed to specify a model. There are...

If i have a program, how can i find the computational complexity? is there some other program i can run in the background?

hi I just wondered if anyone has a sound set of methodologies they apply in their daily life that helps them effectively deal with complexity in life. I feel for every person this set of principles would be different because of they way they are and the way their enviornment is. But perhaps...

The twin paradox is very confusing, and even after reading the explanation, I still get questions. The only explanation of the paradox is when an object is first moving away from earth, and then moving towards the earth. They make it very complicated. How about just moving one direction, and...

It seems to be a law of nature that all things consist of smaller, less complex things: fundamental particles are (comparatively) simple. They react to form atoms, atoms form molecules, molecules form different chemicals, these chemicals also reach with each other to form cells, minerals, etc...

'Schoolbook' multiplication takes O(n^2) operations. Karatsuba multiplication takes O(n^{\lg 3})\approx O(n^{1.59}) operations. The best method I know of (which is only practical for very large numbers) is O(n \log n \log\log n). Is there a known nontrivial lower bound on the complexity of...

While I know the time complexity for all known prime factorization algorithms is exponential, I can't seem to get this results for a very simple algorithm. First assume we're doing this with numbers that are simply the product of two primes (the kind you get when working with RSA and others)...

\frac{<N!>}{<(N-n)!>} = <N^n> (1 + \mathcal{O}( \frac{1}{<N!>} )) The popup you get from clicking on this is missing lots of the code. I presume because my browser is trying to render things as HTML tags.

Every number can be considered a bit string. For a bit string one can define some algorithmic complexity (the shortest algorithm/program that reproduces the desired bit string). Can something be said, in general, about difference in complexity for primes as compared to composites?

I'm looking for some good definitions/ explanations of the two words reductionism and complexity. As I once read reductionist say emergent properties and complex behaviour are epistemological issues, necessary conceptualisations to make the world understandable. Any additional non-physical...

Can you write an example where a space complexity of any number-theoretic algorithm is calculated? Thanks In Advance.

Complexity: distinctions of synonyms of "original" Assume everything (not as a single set but individually or a subsets of the universe) can be derived from something else. T or F ? Assume this is true (T). The word original is defined as : If such is the case with all things that...

Do you think that given time, organisms become more and more complex no matter how slow the evolution of complexity is, organisms do get more complex over time?

does nature or nurture shape us? isn't it just both?

[FONT=Georgia]I have been given an assignment, a small one, which simply takes in number of points in cartesian coordinate format: (x, y) - then - the assignment specified that the program needed to calculate distances of every permutation possible - then return with the set(s) of points that...

i am ineterested in complexity concept do u know any introductory documan on net ...

In Sipser, "Introduction to the Theory of Computation", a proof that "every t(n) time nondeterministic single-tape Turing machine (where t(n) ≥ n) has an equivalent 2O(t(n)) time deterministic single-tape Turing machine" shows that the running time of the equivalent NTM is O(t(n)b^{t(n)}) and...

Its an open question, To my little brain LQG is the only contender, even though it is still an ongoing work. I have read lots about ST, but as someone pointed out, you can not understand it without understanding the maths, but why is it so complex? Surly beautiful theories are easy to...

The term "complexity" is currently used in the study of non-linear dynamics. The main problem with this term arises when is applied to biological systems. For example, does evolution generate ever more complex organisms? A good measure of complexity is lacking. We can observe complexity at...

Let's say f(n) = O(g(n)), i.e. f(n) < cg(n) for some n > n_0. Does the n_0 have to be a precise point of intersection of cg(n) and f(n) or just any point for which n > n_0? Thanks in advance.

Hello, I am trying to understand how to solve problems relating to time complexity of algorithms, esp. problems of the following kind: An algorithm takes 0.5 ms for input size 100. How long will it take for input size 500 if the running time is the following: linear, nlogn, n^2, N^3 An...

Hello, I don't see any specific forum about chaos, self-organised complexity, emergence etc Are there any particular reasons why? How is currently the status / reputation of these fields among scientists? Time ago I read that they couldn't yet deploy any actual theorems in the mathematical...

Hello people, I've been wondering a lot what the string theory equations look like. I have asked this question a while ago and no one answered, so I am guessing its a hard question. But if anyone could answer I woudl be greatfull..thanks. :smile: :smile:

Let us say that we wish to construct and explore a non-trivial numerical form of structural/dynamic abstract or non-abstract complex models. If there was a way to choose the unique building blocks that we need for this goal, it was our gate to the universe of complexity exploration. For...

(Humm where the heck does this thread belong??) Heck proving that "Simplicity breeds Complexity" is about the simplest of things, here, on the net, as all of what you are reading/viewing is simply a collection, a stream, of "ones and zeros" current/no-current (electrical current) and yet its...