2017/09/14 chapter 2.2 in sipser -...

Human-awareRobo.cs

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Pushdown Automata •  2017/09/14

•  Chapter 2.2 in Sipser

Ø  Announcement: q  Slides for this lecture are here:

http://www.public.asu.edu/~yzhan442/teaching/CSE355/Lectures/PDA.pdf

Human-awareRobo.cs

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Last time

FA (DFA & NFA) express Regular Expressions (RE)

•  Context free langauges

o  Context free grammars

q  Design CFGs

q  Ambiguities

q  Chomsky normal form

Ø  Goals:

o  Learned context free grammars: the generator for CFLs

CFL

Human-awareRobo.cs

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Outline for today

FA (DFA & NFA) express Regular Expressions (RE)

•  Context free langauges

o  Context free grammars

o  Pushdown automata

q  Definition of PDA

q  Computation PDA

Ø  Goals:

o  Learn PDA, the computing machine for CFL

CFL

Human-awareRobo.cs

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Pushdown automata

FA:

PDA:

Human-awareRobo.cs

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Pushdown automata

NPDA

Human-awareRobo.cs

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Pushdown automata

Human-awareRobo.cs

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Outline for today

FA (DFA & NFA) express Regular Expressions (RE)

•  Context free langauges

o  Context free grammars

o  Pushdown automata

q  Definition of PDA

q  Computation PDA

Ø  Goals:

o  Learn PDA, the computing machine for CFL

CFL

Human-awareRobo.cs

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Computation of PDA

input string stack

Human-awareRobo.cs

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Computation of PDA

input string stack

$

Human-awareRobo.cs

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Computation of PDA

input string stack

a $

Human-awareRobo.cs

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Computation of PDA

input string stack

a $

Human-awareRobo.cs

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Computation of PDA

input string stack

a a $

Human-awareRobo.cs

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Computation of PDA

input string stack

a $

Human-awareRobo.cs

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Computation of PDA

input string stack

$

Human-awareRobo.cs

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Computation of PDA

input string stack

ACCEPT

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Computation of PDA

input string stack

ACCEPT

what is the language here?

Human-awareRobo.cs

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Computation of PDA

input string stack

ACCEPT

what is the language here? { anbn | n = 0, 1, … }

Human-awareRobo.cs

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Computation of PDA

Human-awareRobo.cs

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Computation of PDA

•  Why do we need the $ sign for stack?

•  Does the stack have to be empty to accept?

•  What if a PDA only pushes and never pops?

•  What if a PDA always pops after pushes?

•  What if a PDA can only keep one symbol on the stack?

Human-awareRobo.cs

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Example

Human-awareRobo.cs

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Example

{ a+b }

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Example

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Example

{ ambn | } m n 2m,m > 0

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Outline for today

FA (DFA & NFA) express Regular Expressions (RE)

•  Reading assignment for the next class:

o  Sipser Sec. 2.2 (remaining) – Quiz link will

be sent out; due date is before the

beginning of the next class on Sep 21

CFL

•  Context free langauges

o  Context free grammars

o  Pushdown automata

q  Definition of PDA

q  Computation PDA

Ø  Goals:

o  Learned PDA, the computing machine for CFL