5.3 Mapping Reducibility (continued)


The Emptiness Problem

What's the Emptiness Problem for Turing Machines?

	E[TM] = { <M> | M is a TM and L(M) = empty-set }

Describe a machine that maps any <M,w> in A[TM] to <M2> in E[TM].

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

What's the problem with these results?
What do you conclude about mapping reduction?

















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) }