lecture 11uofh - cosc 3340 - dr. verma 1 cosc 3340: introduction to theory of computation university...

Lecture 11 UofH - COSC 3340 - Dr. Verma1

COSC 3340: Introduction to Theory of Computation

University of Houston

Dr. Verma

Lecture 11

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Push Down Automaton (PDA)

Language Acceptor Model for CFLs It is an NFA with a stack.

Finite State

controlInput

Stack

Accept/Reject

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PDA (contd.)

In one move the PDA can :– change state,– consume a symbol from the input tape or ignore it– pop a symbol from the stack or ignore it– push a symbol onto the stack or not

A string is accepted provided the machine when started in the start state consumes the string and reaches a final state.

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PDA (contd.)

If PDA in state q can consume u, pop x from stack, change state to p, and push w on stack we show it as

q0

u, x w

q1

u, x ; w In JFLAP

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Example of a PDA

PDA L = {anbn |n 0}

Push S to the stack in the beginning and then pop it at the end before accepting.

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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JFLAP Simulation

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Definition of PDA

Formally, a PDA M = (K, , , , s, F), where– K -- finite set of states -- is the input alphabet -- is the tape alphabet– s K -- is the start state– F K -- is the set of final states (K X X ) X (K X )

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Definition of L(M)

Define * as:(1) *(q, , ) = {(q, , )} {(p, , ) |((q, , ), (p, )) }

(2) *(q, uv, xy) = U {*(p, v, wy) | ((q, u, x), (p, w)) }

i.e., first compute * for all successor configurations and then take the union of all those sets

M accepts w if (f, , x) in *(s, w, ) Alternative: if (f, , ) in *(s, w, ) [we use] L(M) = {w * | M accepts w}

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Example

What is L(M)?

Push S to the stack in the beginning and then pop it at the end before accepting.