(Regular or Not?) Let L {0,1} be a regular language, and wrev to be the reverse of the string w. For each of the languages below, prove whether or not each is regular or not regular, and explain your answer. All points are devoted to the explanation! (Hint: exactly 4 of the languages are always regular).

(a) {wxw:w,x{0,1}}.

(b) {wxw : w,x {0,1},|x| 1}.

(c) {wxw : w,x {0,1},|x| 1,|w| 1}.

(d) {ww : w {0}}.

(e) {ww:w{0,1}}.

(f) {w:wrevwL}.

(g) The language of regexes with unbounded depth of nested parentheses/brackets (see Prob- lem 1).