CS25 Lecture Presentation 6

7/24/2019 CS25 Lecture Presentation 6

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CS 25Automata Theory & Formal Languages

Lecture 6


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PUSHDOWN AUTOMATA

The PDA is an automaton equivalent to the CFG inlanguage-deining !o"e#$

Only the nondeterministic PDA defines all the CFLs.

But the deterministic version models parsers. Most programming languages have deterministicPDAs.


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PUSHDOWN AUTOMATA

A !ushdo"n automata %PDA& is essentiall' an NFA "ith asta()$

On a t#ansition the PDA*

+$ Consumes an in!ut s'm,ol$

$ Goes to a ne" state %o# sta's in the old&$

.$ /e!la(es the to! o the sta() ,' an' st#ing %does nothing0 !o!sthe sta()0 o# !ushes a st#ing onto the sta()&


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PUSHDOWN AUTOMATA

Schematic of a pushdown automaton


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FO/MA1 D2F3N3T3ON OF APUSHDOWN AUTOMATON %PDA&

A !ushdo"n automaton is a 4-tu!le (Q, , !,

, "#, F)0 "he#eQ, , !and Fa#e all inite sets0 and

$% Qis the set o states

2% is the in!ut al!ha,et

% !is the sta() al!ha,et

: Q ' ( ' !() *+Q ' !(is the t#ansition un(tion

5% "#Qis the sta#t state0 and

-% FQis the set o a((e!t states


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TRANSITION FUNCTION : Q ' ( ' !() *+Q ' !(

a!es three arguments"

#. A state$ in Q.

%. An input$ &hich is either a sym'ol in or .

(. A stac! sym'ol in .

)", a, .* is a set of +ero or more actions of the form

)p, *.

pis a state, is a string of stac! sym'ols.


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Actions of the PDA

-f )", a, .* contains )p, * among its actions$ then one thingthe PDA can do in state q$ &ith a at the front of the input$

andZon top of the stac!is"#. Change the state top.

%. emove a from the front of the input )'ut a may 'e *.

(. eplaceZon the top of the stac! 'y .


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25AMP12 OF PUSHDOWN AUTOMATA

EXAMPLE 1* A o#mal des(#i!tion o the PDA o# the language {0n1n|n 0}

1et *+,e %60 70 800 q+0 F&0 "he#e

6 9 :q+0 q0 q.0 q;

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CS25 Lecture Presentation 6