example
Download
Skip this Video
Download Presentation
Example:

Loading in 2 Seconds...

play fullscreen
1 / 3

Example: - PowerPoint PPT Presentation


  • 92 Views
  • Uploaded on

Example:. Given the following CFG S  X | Y X  aXb | aX | a Y  aYb | Yb | b (1) L(G) = ? (2) Design an equivalent PDA for it. Σ ={a, b}. Solution: L(S). S  X | Y X  a X b | a X | a Y  a Y b | Y b | b.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Example:' - waylon


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
example
Example:
  • Given the following CFG

S  X | Y

X  aXb | aX | a

Y  aYb | Yb | b

  • (1) L(G) = ?
  • (2) Design an equivalent PDA for it.

Σ={a, b}

solution l s
Solution: L(S)

S  X |Y

X aXb | aX | a

Y aYb | Yb | b

Try to write some strings generated by it:

SXaXbaaXbbaaaXbbaaaabb

SYaYbaYbbaaYbbbaabbbb

more a’s than b’s

more b’s than a’s

  • Observations:
  • Start from S, we can enter two States X & Y, and X, Y are “independent”;
  • In X state, always more a are generated;
  • In Y state, always more b are generated.

Ls = Lx U Ly

L(S) =

{ aibj; i≠j }

Lx = { aibj; i>j }

Lx = { aibj; i

solution pda
a,e/A

b,A/e

b,$/$

a,e/A

b,A/e

e,A/e

e,$/e

e,$/e

e,e/e

e,e/$

e,e/$

e,e/e

e,A/e

b,$/$

q0

q’0

q1

q’1

q2

q’2

q3

q’3

Solution: PDA

L(S) = { aibj; i≠j }

S  X | Y

X aXb | aX | a

Y aYb | Yb | b

= { aibj; i>j } U { aibj; i

PDA = NFA + a stack (infinite memory)

A possible way: “divide and conquer”

Lx = { aibj; i>j }

LY = { aibj; i

e, e /e

Combine both …

ad