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.


	L3 = { <M> | M is a TM which accepts some string of 1s and 0s
				containing an odd number of 1s }