The Halting Problem
Undecidable Problems From Language Theory
EQT M = {< M1 , M2 > | M1 and M2 are TMs and L(M1 ) = L(M2 )}
Theorem EQT M is undecidable. • Suppose that R is a decider for EQT M .
We construct TM S to decide ET M as follows: S = “On input < M >, where M is a TM: 1. Run R on input < M, M1 >, where M1 is a TM that rejects all inputs. 2. If R accepts, accept; if R rejects, reject. • If R decides EQT M , then S decides ET M .