The problem of determining whether a given Turing machine has an equivalent finite automaton is decidible

Suppose that the Turing machine R decides E_{LBA}, then we could construct the Turing machine S to decide A_{TM} as follows.

S = “On input ⟨M, w⟩, where M is a Turing machine and w is a string:

1. Construct LBA B from M and w.

2. Run R on input ⟨B⟩.

3. If R rejects, reject; if R accepts, accept.”

The undecidability of A_{TM} can be used to prove the undecidability of the halting problem by reducing  A_{TM} to  HALT_{TM}

The Post Correspondence Problem is solvable by algorithms.

if there is a Turing machine M such that L(M)=L and M halts at every point then L is a 

Every context-free language is also a decidable language