Please draw the dfa diagram for me$.$ a proper diagram on paper with transition table for part b

a$.$ The following instance of Post's correspondence does not have a solution. Give an explanation why

no solution can exist for this instance.

$\{(abb,ab),(a,b),(ab,aa)\}.$

b$.$ Construct a DFA that accepts all binary words that are not divisible by $5.$

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.

d$.$ Briefly explain in one or two paragraphs what does it mean for a problem to be undecidable?