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  • Apr 20 : First Lecture on Jul 28, 2025, at 8 AM in CS36
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Meetings  

Click on the theme item for the meeting plan for that theme.
Click on the meeting item for references, exercises, and additional reading related to it.
  • Theme 1 : Basic Computability - 9 meetings

    • Meeting 01 : Mon, Jul 28, 08:00 am-08:50 am
      • Brief introduction to the course and the contents. Administrative Announcements. Grading policies. Languages vs Algorithmic Problems. Automata theory vs algorithms courses. Historical aspects of the idea of computation. Ruler and Compass problem. Hilbert's program. Formal model of computation. Post Systems, Mu-calculus, Lambda calculus. Turing machines. Church-Turing thesis.

    • Meeting 02 : Tue, Jul 29, 12:00 pm-12:50 pm
      • Formal Model of Turing machines. Nuances of the definition. Configurations of a Turing Machine.

    • Meeting 03 : Thu, Jul 31, 11:00 am-11:50 am
      • Language accepted by Turing machines. Total Turing machines. Algorithms vs Turing machines. Drawbacks. Diophantine problem. Is there a computational task that total Turing machines cannot do? Two observations about TM model (1) encoding a TM as a string (2) Universal TM.

    • Meeting 04 : Fri, Aug 01, 10:00 am-10:50 am
      • Review of Cantor's diagonalization and infinities. The infinite matrix form. Entry filling task. Impossibility proof.

    • Meeting 05 : Mon, Aug 04, 10:00 am-10:50 am
      • Undecidability of HP. The language MP and undecidability through mimicking the diagonalization.

    • Meeting 06 : Tue, Aug 05, 12:00 pm-12:50 pm
      • MP vs HP. Building HP-solver using MP-solver. Building MP-solver using HP-solver. Two different methods. Reductions and many-one reductions.

    • Meeting 07 : Thu, Aug 07, 11:00 am-11:50 am
      • Recap of reductions. A and A-bar are semidecidable if and only if A is decidable. The complement of MP is outside SD. The CoSD class. SD intersection CoSD is exactly the decidables. MP cannot many-one reduce to MP-har.

      MP_42 language. Undecidability of MP_42. The generic nature of the reduction.

    • Meeting 08 : Fri, Aug 08, 10:00 am-10:50 am
      • Demonstrating the generality of the idea. FULL, REG, CFL, DEC, FIN are all undecidable. MP reduces to REG, MP reduces to REG-bar. The first language outside the SD and CoSD.

    • (Upcoming) Meeting 09 : Mon, Aug 11, 08:00 am-08:50 am
      • Rice's theorems.