5.3 Mapping Reducibility (continued)


The Equivalence Problem

What's the Equivalence Problem for Turing Machines?

	EQ[TM] = { <M1, M2> | M1 and M2 are TMs and L(M1) = L(M2) }

Describe a machine that maps any w in E[TM] to f(w) in EQ[TM].

If <M> is in E[TM], how do you show <M,M2> is in EQ[TM]?
If <M> is not in E[TM], how do you show <M,M2> is not in EQ[TM]?

Write the proof that EQ[TM] is Undecidable.

















Classwork
You may work with a partner.

Use a mapping reduction to prove the language is Undecidable.


	L4 = { <M> | M is a TM and M accepts any string of
	       1s and 0s that contains both 1s and 0s (M doesn't
	       accept strings that contain only 1s or only 0s) }