Turing Machines & Undecidability

  1. 1. The problem statement, all variables and given/known data

    I have a question regarding undecidable languages.
    Let L1 = { M | M is an encoding of a Turing machine that accepts any input} and L2 = { M | M is an Turing machine with at most 100 states}. Is L1 intersect L2 decidable?

    2. Relevant equations

    3. The attempt at a solution

    I think L1 is undeciable and L2 is decidable. Since we can have a many-to-1 reduction from halting to L1 and for L2, we can count the number of states in some encoding. And I guess L1 intersect L2 is still undecidable but I can't find a reduction to any undecidable problems.

    Any help will be appreciated!
  2. jcsd
  3. I mean partially decidable or recursively enumerable.
  4. Aren't they both regular?
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