Final answer:
The given question is about designing an automaton that recognizes words over the alphabet {a,b,c} with certain conditions.
Step-by-step explanation:
The given question is about designing an automaton that recognizes words over the alphabet {a,b,c} with certain conditions. The automaton should ensure that every 'a' is followed by at least one 'b', every 'c' is preceded by at least one 'b', and the last letter of the word is either a 'b' or a 'c'.
This question falls under the topic of Automata Theory in Mathematics. An automaton is a formal model for a computation, and designing one that recognizes specific patterns in a given set of symbols is an important concept in this field.
In summary, this question is about designing an automaton that recognizes words over an alphabet and satisfies certain conditions.