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What is a Queue Automaton?
<p>A queue automaton is like a push-down automaton (PDA) except that the stack is replaced by a queue.</p><ul class="list"><li><p>A queue is a tape allowing symbols to be written only on the left-hand end and read only at the right-hand end.</p></li><li><p>Each write operation (we’ll call it a push) adds a symbol to the left-hand end of the queue and each read operation (we’ll call it a pull) reads and removes a symbol at the right-hand end.</p></li><li><p>As with a PDA, the input is placed on a separate read-only input tape, and the head on the input tape can move only from left to right.</p></li><li><p>The input tape contains a cell with a blank symbol following the input, so that the end of the input can be detected.</p></li><li><p>A queue automaton accepts its input by entering a special accept state at any time.</p></li></ul><h2>Formal Definition</h2><p>A deterministic queue automaton (DQA) is defined as a seven tuple</p><pre class="result notranslate">(Q, Σ, Γ, δ, q0 , ⊥, F)</pre><p>Where,</p><ul class="list"><li><p>Q is a set of states,</p></li><li><p>Σ is an input alphabet,</p></li><li><p>Γ is a finite set of queue symbols,</p></li><li><p>q0 is a starting state,</p></li><li><p>⊥ is an empty queue symbol ⊥6= Γ,</p></li><li><p>The transition function δ is defined by Q × Σ ∪ {λ} × (Γ × Γ) ∪ ({⊥} × {⊥}) → Q × Γ ∪ {λ} × {keep, remove}, where λ signifies empty symbol. It must never be used as an input symbol.</p></li><li><p>F is a set of accepting states (F ⊆ Q).</p></li></ul><h2>Example</h2><p>Construct queue automata for language {a<sup>n</sup>b<sup>n</sup> | n >= 0}.</p><p>For the given language the number of states present in the automata are 4,</p><p>Q={q0,q1,q2,q3},</p><p>Input alphabet ={a,b}</p><p>The queue automata is as follows −</p><p><img src="https://www.tutorialspoint.com/assets/questions/media/53248/Queue.jpg" class="fr-fic fr-dib" width="322" height="225"></p>
Updated on 15-Jun-2021 12:17:12
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