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Limits of Computation

The limits of computation are governed by a number of different factors. In particular, there are several physical and practical limits to the amount of computation or data storage that can be performed with a given amount of mass, volume, or energy.

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Types of Problems and Context

There exists two types of algorithms - tractable and intractable. A tractable problem can be solved within a useful period of time. Tractable problems have a polynomial or less time solution. Intractable problems are theoretically solvable (i.e. there exists a corresponding algorithm) but are classified as ‘insoluble’ due to limits of computations - due to the speed of today’s technology, it may take millions of years to solve. Intractable problems do not have a polynomial (or less) time solution.

They cannot be solved within a useful period of time. For these types of problems, we may use a heuristic method. These are approximate solutions to a problem; they are not optimal, but are more useful than their intractable equivalent.

Additional Reading

Be Inspired - when Algorithms fail - AI and Algos