Hint: The C_{2} case is trivial, since we can detect divisibility by 2 just by looking at the least significant bit. First show that C_{3} is regular. Then argue that your method generalizes to any integer n ≥ 3.
L_{2} = { a^{i} b^{j} c^{k} | i ≠ j or j ≠ k }Note: a high-level English description of your PDA has comments like "push X whenever a 0 is read."
A = { x ∈ {0,1}^{*} | x has exactly three 0's, the length of x is odd and the middle symbol of x is 0. }
COF = { < M > | M is a TM and L(M) is cofinite}Prove that FIN ≤_{m} COF. That is FIN reduces to COF via a many-one reduction (a.k.a. a "mapping" reduction).
FIN = { < M > | M is a TM and L(M) is finite}
EQUIV_{TM} = { ⟨ M_{1}, M_{2} ⟩ | L(M_{1}) = L(M_{2}) }
K_{17} = { ⟨ M ⟩ | L(M) contains at least 17 strings }
Note: as a consequece K_{17} is undecidable.
EQ_{17} = { ⟨ M ⟩ | L(M) contains exactly 17 strings }
Note: as a consequece EQ_{17} is not Turing-recognizable.