a. The following instance of Post's correspondence does not have a solution. Give an explanation why no solution can exist for this instance. {(abb,ab),(a,b),(ab,aa)}. [5 marks] b. Construct a DFA that accepts all binary words that are not divisible by 5. [10 marks] c. Briefly explain in one or two paragraphs how to construct a DFA for pattern matching in a text. Explain how the properties of the pattern can be used in the construction. [5 marks] d. Briefly explain in one or two paragraphs what does it mean for a problem to be undecidable? [5 marks]