Titlebook: Limits of Computation; From a Programming P Bernhard Reus Textbook 2016 The Editor(s) (if applicable) and The Author(s), under exclusive li

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978-3-319-27887-2The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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A Self-interpreter for ,that our . language was an acceptable choice for “effective procedures”. The .-language does not provide recursive procedures and therefore we have to implement a traversal of abstract syntax trees using stacks.

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An Undecidable (Non-computable) Problemis undecidable i.e. that no computer program can solve. We define the concept of .-decidability and define the famous Halting problem whether a given .-program terminates when run on a given input. The concept of diagonalisation is explained and then used to prove that the Halting problem is .-undecidable.

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