Many decidable problems can be solved by searching over a large but finite space of possible options. Searching this space might take a staggeringly long time, but only finite time. From a decidability …

Here is a list of some measures of complexity grouped according to the question that they try to answer. Measures within a group are typically closely related quantities.

Simply stated, complexity arises in situations where “an increasing number of independent variables begin interacting in interdependent and unpredictable ways.” Traffic, the weather, the stock market …

Given a Turing machine M, we can define the time complexity tM(x) to be the number of steps the machine runs for before halting, and we define the space complexity sM(x) to be the number of …

That is, whether we choose to study complexity on Turing machines or Random Access Machines, our observations should still hold. They should also be invariant under small changes to the Turing …

Computational complexity is the study of the difficulty of solving computational problems, in terms of the required computational resources, such as time and space (memory).

Complexity science can provide a comprehensive, cross-disciplinary analytical approach that complements traditional scientific approaches that focus on specific subject matter in each domain.