MATHS - Below you will find a question the areas of automata

Below you will find a question the areas of automata. Solve the problem showing all steps. Thoroughly explain how and why you performed each step with complete sentences.

A finite-state automaton is given by the 5-tuple (Q, ∑, δ, q, F), where

Q = the finite set of states = {A, B, C}

∑ = the Alphabet (inputs) = {x, y}

δ = the transition function using the alphabet as inputs to the states

q = the initial state = {A}

F = Accepting (or final) state = {C}

The transition table for the automaton is given by:



δ

δ



x

y

A

A

B

B

A

C

C

A

C

(i). Draw the corresponding transition diagram (digraph).

(ii). Provide 5 strings that are in the language generated by the automaton.

(iii). Provide 5 strings, that use the same inputs, which are not in the language generated by the automata.

(iv). Write a general statement that describes when a string is part of the language generated by the above automata and when that string is not in the language.