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Intro to Theory of Computation

L ECTURE 16 Last time Undecidable /unrecognizable languages ( A TM is undecidable ) Diagonalization Today A TM is unrecognizable Reductions. Intro to Theory of Computation. CS 464. Sofya Raskhodnikova. Classes of languages. recognizable. A TM. decidable. A TM. CFL. regular.

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Intro to Theory of Computation

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  1. LECTURE16 • Last time • Undecidable/unrecognizable languages (ATM is undecidable) • Diagonalization • Today • ATM is unrecognizable • Reductions Intro to Theory of Computation CS 464 Sofya Raskhodnikova Sofya Raskhodnikova; based on slides by Nick Hopper

  2. Classes of languages recognizable ATM decidable ATM CFL regular 1* Sofya Raskhodnikova; based on slides by Nick Hopper

  3. Theorem. Language L is decidable iff L and L are Turing-recognizable Corollary.is not Turing-recognizable. ATM Sofya Raskhodnikova; based on slides by Nick Hopper

  4. Prove that the following language are Turing-recognizable ATM= {is a TM that accepts string } HALTTM= {is a TM that halts on string } Sofya Raskhodnikova; based on slides by Nick Hopper

  5. Prove that the following language are undecidable via reduction from ATM HALTTM= {is a TM that halts on string } ETM= {is a TM and } CFLTM= {is a TM and is context-free} Sofya Raskhodnikova; based on slides by Nick Hopper

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