An Introduction to Algorithmic Information Theory Nuri Taşdemir 17-11-2006.

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Presentation transcript:

An Introduction to Algorithmic Information Theory Nuri Taşdemir

Randomness Random-bit generators Random bits – – –

Complexity Time complexity Space complexity Program-size complexity

Universal computers

CN is an immune set

Prefix-free codes Instantaneous Uniquely decodable

Self-delimiting TM Input tape Work tape Output tape

Probability of obtaining a string on C

Halting Probability Ω

Ω is a solution for Halting Problem Unfortunately Ω is incomputable

Thank you