# Introduction to Queue Automata

• Last Updated : 08 Jul, 2020

We already know about Finite Automata which can be used to accept regular languages and Pushdown Automata that can be used to recognize Context Free Languages.

Queue Automata(QDA) is a non-deterministic automata that is similar to Pushdown Automata but has a queue instead of a stack which helps Queue automata to recognize languages beyond Context Free Languages.

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A QDA is a 6 – tuple Where

1. Q is the set of finite states.
2. is the set of finite input alphabets.
3. is the set of finite queue alphabets.
4. .
5. is the start state.
6. F Q is the set of accept states.

Acceptance of a string

A QDA accepts input if can be written as , where each  and there are states and strings exist, such that they satisfy the following conditions:

1. and .
2. For  and and and 3. Example:
Define the queue automata for language Solution:
Q = {q0, q1, q2, q3} and ={a, b} and = {a, b, $} And the transition functions are given by:       Let us see how this automata works for aabb. RowStateInputTransition functionQueue(Input from left)State after move 1q0aabbδ(q0, a, ε)={(q0, a)}aq0 2q0aabbδ(q0, a, ε)={(q0, a)}aaq0 3q0εδ(q0, ε, ε)={(q1,$)}$aaq1 4q1εδ(q1, ε, a)={(q2, ε)}$aq2
5q2εδ(q2, ε, a)={(q2, a)}a$q2 6q2aabbδ(q2, b,$)={(q1, $)}$aq1
7q1εδ(q1, ε, a)={(q2, ε)}$q2 8q2aabbδ(q2, b,$)={(q1, $)}$q1
9q1εδ(q1, ε, $)={(q3,$)}\$q3

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