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.
A QDA is a 6 – tuple
Where
- Q is the set of finite states.
-
is the set of finite input alphabets. -
is the set of finite queue alphabets. -
. -
is the start state. -
F
Q is the set of accept states.
Acceptance of a string
A QDA
-
and . - For
and and and
Example:
Define the queue automata for language
| Row | State | Input | Transition function | Queue(Input from left) | State after move |
|---|---|---|---|---|---|
| 1 | q0 | aabb | δ(q0, a, ε)={(q0, a)} | a | q0 |
| 2 | q0 | aabb | δ(q0, a, ε)={(q0, a)} | aa | q0 |
| 3 | q0 | ε | δ(q0, ε, ε)={(q1, $)} | $aa | q1 |
| 4 | q1 | ε | δ(q1, ε, a)={(q2, ε)} | $a | q2 |
| 5 | q2 | ε | δ(q2, ε, a)={(q2, a)} | a$ | q2 |
| 6 | q2 | aabb | δ(q2, b, $)={(q1, $)} | $a | q1 |
| 7 | q1 | ε | δ(q1, ε, a)={(q2, ε)} | $ | q2 |
| 8 | q2 | aabb | δ(q2, b, $)={(q1, $)} | $ | q1 |
| 9 | q1 | ε | δ(q1, ε, $)={(q3, $)} | $ | q3 |