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Is there a way to convert a deterministic pushdown automata into a turing machine? I thought about putting the stack after the input on the tape, with '#' between them. But it seems kind of impossible to prove it formally.

Do you have any suggestions? Did somebody do it already?

Thank you

Blacklight Shining
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pepper potts
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  • on input-tape do `STACK-SYMBOLS # INPUT STRING` For input symbol read also read leftmost symbol from left hand side (note you have to memorized the current input symbol in the form of states) We knows input symbols are finite. – Grijesh Chauhan May 29 '13 at 12:41

1 Answers1

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Push-down automaton works only in one direction. That is it cannot retrace its step or keep a count.
For example, if you want a formal language: 

L = {1^n+0^m | n>m, m>0}

Here the no. of 1's are greater than no. of zeroes.
This problem is solvable by both DPDA and Turing Machine.

However if we add another condition, like: 

L = {1^n.0^m.1^n | n>m, m>0}

Assuming that you know how to solve the above problem in Turing Machine, you would understand its not possible to solve it without back tracing the input tape.
Therefore there is no way you can make PDA as powerful as Turing Machine.
Here is link to Wiki for your more understanding :https://en.wikipedia.org/wiki/Chomsky_hierarchy

olibiaz
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Jahangir Ali
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