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Summary: Theory of Computation
Lecture 13: Undecidable Languages
Max Alekseyev
University of South Carolina
March 1, 2012
Decidable vs. Undecidable Languages
EQDFA = { A, B | A, B are DFAs and L(A) = L(B)}
EQCFG = { G, H | G, H are CFGs and L(G) = L(H)}
We proved that EQDFA is decidable. In contrast to EQDFA, it is
not clear how to prove that EQCFG is decidable.
Decidable vs. Undecidable Languages
EQDFA = { A, B | A, B are DFAs and L(A) = L(B)}
EQCFG = { G, H | G, H are CFGs and L(G) = L(H)}
We proved that EQDFA is decidable. In contrast to EQDFA, it is
not clear how to prove that EQCFG is decidable.
In fact, it is NOT decidable. But it is still unclear how to prove
that.
Our goal is to prove undecidability of another somewhat "simpler"
language
ATM = { M, w | M is a TM and M accepts w}
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