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A PDA (Pushdown Automaton) is said to be k-turn if, for any string w in its language, turn the direction of its stack at most for k times. Also it is well-known that the language L is linear iff accepted by a 1-turn PDA. Now, is it true that the regular languages are the languages which are accepted by a 0-turn PDA?

Jonathan Leffler
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M.K. Dadsetani
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1 Answers1

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Yes,
You can think a finite automata as a kind of 0-turn PDA in which a stack is never used.

A PDA is said to perform a turn if the stack goes up and down respectively in two consecutive descriptions of the automata. And for every Regular language a PDA can be constructed in which we empties PDS at the end of string acceptance.

Also, Regular Language is subset of Linear Languages in Chomsky classification (either Right linear or Left linear).

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Grijesh Chauhan
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  • its good, but what about the converse? I mean how u can show that a 0-turn language is regular? maybe in this way: for a given pda with states=Q and stack symbols=G, construct a dfa with states=Q\times G, then the dfa move from (p,X) to (q,Y) by reading symbol 'a', if the pda move from (p,aw,X) to (q,w,Y). – M.K. Dadsetani Dec 15 '12 at 08:19
  • Yes you are correct..An Finite Automate with `N` states can be simulate as `PDA` of `2 states` and `N stack symbol`. The reverse is what you said. – Grijesh Chauhan Dec 15 '12 at 13:10