# day38 - Consequences We cannot decide if the set of valid...

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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 11 Consequences We cannot decide if the set of valid terminating traces of an arbitrary machine M are finite. Put differently, we cannot decide if there is an upper bound on the length of any valid trace.

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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 22 1981, Again Theorem 5: The problem to determine, for an arbitrary context free language L, if there exist a finite n such that Ln = Ln+1 is undecidable.
10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 33 L for Machine M L1 = { C1# C2R \$ | C1, C2 are configurations }, L2 = { C1#C2R\$C3#C4R … \$C2k- 1#C2kR\$ | where k ° 1 and, for some i, 1 - i < 2k, Ci -M Ci+1 is false }, L = L1 ° L2 “ {° }.

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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 44 Finite Power Property L is context free. Any product of L1 and L2, which contains L2 at least once, is L2. For instance, L1 ° L2 = L2 ° L1 = L2 b L2 = L2. This shows that (L1 ° L2)n = L1n { L2. Thus, Ln = {J} ° L1 ° L12 … ° L1n V L2.
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