HU = Introduction to Automata Theory, Languages and Computation, Hopcroft & Ullman, 1979.
Note: for people with the first printing of the textbook, Ex 1.17(b) should read "{ www | ...}" (3 w's instead of 2).
Note: for people with the first printing of the textbook, in Prob 1.23(d), the string w is in {0,1}* (the * is missing).
Optional: [HU Ex 3.18, p. 73] Show that if L is regular, then so is the following language:
LOG(L) = { x | for some y with |y| = 2^{|x|}, xy is in L }
K_{17} = { <M> | <M> is an encoding of a Turing machine and |L(M)| >= 17 }
ALL_{TM} = { <M> | <M> is an encoding of a Turing machine and L(M) = Sigma^{*} }
INF_{TM} = { <M> | <M> is an encoding of a Turing machine and L(M) contains an infinite number of strings}
A set is cofinite if it is the complement of a finite set. Let
COF = { < M > | M is a TM and L(M) is cofinite}
FIN = { < M > | M is a TM and L(M) is finite}
Prove that FIN reduces to COF via a many-one reduction.