What is the language recognized by the given deterministic finite-state automaton. Start so Link to the image the set of bit strings containing an even num- ber of 1s and an odd number of Os. O the set of bit strings consisting of a O followed by a string with an odd number of 1s. Othe set of all bit strings that contain an even num- ber of Os and an odd number of 1s. the set of all bit strings that contain an odd number of Os None

Q5: Design a PDA for accepting a language (0"1"0 | m, n-1} give the ID form as we explain in the lecture. Apply the string "00011000" on this PDA using ID transitions.

please explain.

The operation Perm(w), applied to a string w, is all strings that can be constructed by permuting the symbols of w in any order. For example, if w= 101, then Perm(w) is all strings with two l's and one 0, i.e., Perm(w) = {101, 110, 011). If L is a regular language, then Perm(L) is the union of Perm(w) taken over all w in L. For example, if L is the language L(0*1*), then Perm(L) is all strings of 0's and 1's, i.e., L((0+1)*). If L is regular, Perm(L) is sometimes regular, sometimes context-free but not regular, and sometimes not even context-free. Consider each of the following regular expressions R below, and decide whether Perm(L(R)) is regular, context- free, or neither: 1. (01)* 2.0*+1* 3. (012)* 4. (01+2)* a) Perm(L(0*+1*)) is context-free but not regular. O b) Perm(L((01+2)*)) is context-free but not regular. c) Perm(L((01+2)*)) is not context-free. O d) Perm(L((01)*)) is regular.