This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: ’ accepts the input which simulates the accepting computation history of M with input x.) M M ’ configuration # C # C 1 # … C f # X LBA M ’ works as follows: On input x: (1) Check C is the initial configuration of M with input w; (2) C i C i+1; (3) C f is an accepting configuration for M. If all true then M ’ accepts the input x, otherwise M ’ reject x. M ’ accepts x iff M accepts w ( x is an accepting computation history for M on w) L(M ’ ) ≠φ iff <M, w> ∈ L U <M ’ > ∈ A NE iff <M, w> ∈ L U Now we are ready to state the reduction of A TM to A NE . Suppose that TM R decides A NE. Construct TM S that decides A TM as follows. S=“ On input <M,w>,where M is a TM and w is a string: (1)Construct LBA M ’ from M and w as described above. (2)Run R on input < M ’ >. (3)If R rejects, accept; if R accepts, reject.” Theorem: PCP is undecidable Proof: PCP simulates TM computation...
View Full Document
- Spring '04
- Halting problem