<p>It's not part of the normal definition of PDA, but it is an "equivalent" definition: If we say a PDA is something that can only push one symbol at a time, let's call yours a "Push-multiple-down Automata" , or PMDA. :) </p>

<p>Then you can show than any PDA is also a PMDA (that part is trivial), and that any PMDA can be turned into an equivalent PDA. The conversion consists of adding states for "pushing down a few at a time". So for instance, if I at some point should push the string "adbd", then I add in 3 extra states $s_1 \dots s_3$. I start by pushing "a" and transitioning to $s_1$, then from $s_1$ I push "d" and transition to $s_2$, and so on; and after pushing from $s_3$ I end up and the end state that the PMDA would have transitioned to in a single step.</p>

<p>Thus, pushing multiple symbols might be convenient in some descriptions, but doesn't alter the power of the machine. This is why it's usually not discussed.</p>

CC BY-SA 3.0
2018-04-08T21:31:56.093Z
2018-04-08T21:31:56.093Z
Alex Meiburg
<p>Can we put more than one element in stack at a time.
Actually I am asking that this transition function is valid for PDA:
∆(q,a,z)=(q',aaz)
Where:</p>

<ol>
<li>q and q' are states</li>
<li>a is input symbol</li>
<li>z is starting stack symbol</li>
<li>This transition function is doing that if PDA is in q state and read input a and top element of stack is z then it goes to state q' and put aa in stack.
Is above transition. Function is valid for PDA.
And my college teacher said that it is true but I have never read this in any book that it is true neither I have read this is false.</li>
</ol>

<automata-theory>
Push Down Automata
user49174
# Push Down Automata

(Asked by: username_0 on 2018-04-08)

Can we put more than one element in stack at a time.
Actually I am asking that this transition function is valid for PDA:
∆(q,a,z)=(q',aaz)
Where:

1. q and q' are states
2. a is input symbol
3. z is starting stack symbol
4. This transition function is doing that if PDA is in q state and read input a and top element of stack is z then it goes to state q' and put aa in stack.
   Is above transition. Function is valid for PDA.
   And my college teacher said that it is true but I have never read this in any book that it is true neither I have read this is false.

**Tags:** automata-theory


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## 1 answers

### Answer by username_1 on 2018-04-08. Score: 1

It's not part of the normal definition of PDA, but it is an "equivalent" definition: If we say a PDA is something that can only push one symbol at a time, let's call yours a "Push-multiple-down Automata" , or PMDA. :)

Then you can show than any PDA is also a PMDA (that part is trivial), and that any PMDA can be turned into an equivalent PDA. The conversion consists of adding states for "pushing down a few at a time". So for instance, if I at some point should push the string "adbd", then I add in 3 extra states $s\_1 \dots s\_3$. I start by pushing "a" and transitioning to $s\_1$, then from $s\_1$ I push "d" and transition to $s\_2$, and so on; and after pushing from $s\_3$ I end up and the end state that the PMDA would have transitioned to in a single step.

Thus, pushing multiple symbols might be convenient in some descriptions, but doesn't alter the power of the machine. This is why it's usually not discussed.


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