Let A be a DFA that accepts all strings over the alphabet {1,0} that contain either the substring 10 or 01 (non-exclusive, i.e. both can be contained as substrings)., and consider the string w = 001011. Confirm that w L(A) , by showing that (p0, w) F where q0 is the start state of A and F is its finish states. You have to show this formally using the inductive definition of . (Start with (q0, 0) and then (q0, 00) and then (q0, 001) and so on...)

Formally, we define 8* : QXE* Q using the following inductive definition: . 8* (q, ) = q for every q EQ 8*(q, wa) = 8(*(q, w), a) for each q E Q,WEE, a e Note that by the above definition of 8*, we have that we L(M) iff 8(90,w) EF