September 22

September 22 - CSCI 2670 Introduction to Theory of...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
CSCI 2670 Introduction to Theory of Computing September 22, 2005
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
September 22, 2005 Agenda •Yester day –Pushdown automata •Today – Equivalence of pushdown automata and
Background image of page 2
September 22, 2005 Announcements • Matrix Reloaded tonight! – 6:30 in Boyd 328 • Free popcorn • 25 cent Coke • Pizza will be ordered at cost if people want
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
September 22, 2005 Equivalence of PDA’s and CFG’s Theorem: A language is context free if and only if some pushdown automaton recognizes it Proved in two lemmas – one for the “if” direction and one for the “only if” direction We will only do the “only if” step – i.e., show that every context-free language has an associated PDA
Background image of page 4
September 22, 2005 CFG’s are recognized by PDA’s Lemma: If a language is context free, then some pushdown automaton recognizes it Proof idea: Construct a PDA following CFG rules
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
September 22, 2005 CFG’s are recognized by PDA’s Format of the new PDA q start q loop q accept ε , ε S$ ε ,$ ε a,a ε ε ,A w Start by pushing the start variable and stack bottom marker Have a transition for each rule replacing the variable with its right hand side Have a transition that allows us to read each alphabet symbol if it is at the top of the stack Finish only if the stack is empty
Background image of page 6
September 22, 2005 Constructing the PDA • You can read any symbol in Σ when that symbol is at the top of the stack – Transitions of the form a,a ε • The rules will be pushed onto the stack – when a variable A is on top of the stack and there is a rule A w, you pop A and push w • You can go to the accept state only if the stack is empty
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
September 22, 2005 Idea of PDA construction for A xBz State control a b A t State control a b x B z t
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/07/2011 for the course CS 501 taught by Professor Sm during the Spring '11 term at Indiana.

Page1 / 34

September 22 - CSCI 2670 Introduction to Theory of...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online