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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 ) 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...
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- Spring '04