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l11-handout - Lecture 11 Turing Machines and Undecidability...

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Lecture 11: Turing Machines and Undecidability David Dill Department of Computer Science 1 Outline Recursively enumerable vs. RE. A language that is not RE. Simulation of Turing Machines. 2 Recursive vs. RE Recursively Enumerable Language – accepted when TM enters a final state, rejected otherwise (even if TM loops). Recursive Language – accepted by a TM that always halts, even when it rejects the input. The membership problem for a language is decidable iff the language is recursive. A TM that always halts is called an algorithm . hh Draw circles for Not-RE, RE, Recursive ii 3 Turing machines can make/modify other Turing machines Turing machines can be encoded as strings. Strings can be read and written by Turing machines (so the definition of the machine can be changed). Turing machines can simulate other Turing machines. “Turing machine virtualization” 4
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String encoding and simulation of Turing Machines Turing machines as strings: Find an encoding for Turing machines as strings of 1’s and 0’s (binary encoding).
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