5.1 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) }

What problem will you reduce to EQ[TM]?

Can you build a TM that accepts nothing (rejects everything)?

How do you use an EQ[TM] decider R to build an E[TM] decider S?

	S = "On input <M>, where M is a TM:
	  1.
	  2.
	  3.

Write the proof that EQ[TM] is Undecidable.

















Classwork
You may work with a partner.

Prove that 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) }