1. Finite automata and regular languages (a) Construct a DFA and a regular expression for the language L = {x E {0,1} x contains a (b) Construct a DFA and a regular expression for the language L rE 10, 1) length of r is not (c) Construct a 6-state NFA and a regular expression for the language L-(x E {a,b)" | x ends in substring "100" divisible by 3) "ba" or has exactly two a's J, such that your NFA has at least one e-arrow and also multiple transitions on the same symbo the general construction described in the proof that NFAs can simulate regular expressions in words the language this NFA accepts (d) Construct an NFA from a regular expression ((aU(ab)*)c) over the alphabet a, b, c, using (e) Given the following NFA, construct a DFA using the construction from the classotes. Describe 8-8-8 42