# Transition Diagram for Automaton

Automata theory involves the study of mathematical objects called automata and the computational problems that can be solved using them. Context-free grammar provides us with mathematical techniques of building phases in a language from other blocks that are smaller. Visual structures called parse trees enable us to clearly differentiate which phrases are unique and which ones are ambiguous.

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 the table in the attachment.

(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 given automata and when that string is not in the language.

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#### Solution Preview

(i) Please refer to the attached 575778.jpg for the transition diagram (digraph).

(iv) Any string consisting of any number of x and y that ends with atleast two ys, belongs to the language generated by ...

#### Solution Summary

Response briefly explains the logic behind answer in part (iv), and it gives more than 5 strings in part (iii) that correspond to same inputs in part (ii).