Turing Machines & Undecidability

crazyautomata

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!

Max.Planck

What do you mean by undecible language, the chomsky hiearchy for languages is given as follows: http://en.wikipedia.org/wiki/Chomsky_hierarchy.

crazyautomata

I mean partially decidable or recursively enumerable.

Max.Planck

Aren't they both regular?