Lecture 6 NFA Subset Construction

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Lecture 6NFA Subset Construction Epsilon
Transitions
CSCE 355 Foundations of Computation

• Topics
• Examples Subset Construction
• Authors Website again
• Epsilon transitions
• Ruby - dfa1.rb

Sept 15, 2008
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• Last Time Readings 2.3
• Examples Subset construction converting NFA ?
  equivalent DFA
• e-NFA
• TEST 1 September 29th
• New Readings section 2.2.3-2.4
• Sample Test 1
• Mutual Induction Proof revisited
• Theorem 2.12 Proof
• Authors Website Solutions Online
• e-NFA ? NFA
• e-NFA ? DFA subset construction
• Regular Expressions
• Relations Machines and Regular expressions
• Ruby regular expressions
• Ruby Pickaxe Book
• Ruby showmatch.rb

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Exercise 2.2.9 Solutions Online

• Authors Website for Text
• http//infolab.stanford.edu/ullman/ialc.html
• HW Solutions for starred () problems
• http//infolab.stanford.edu/ullman/ialcsols/sol2.
  html
• 2.2.9 page 54 Prove If d(q0, a) d(qf, a) for
  all a in S then for all w ! e we have d(q0, w)
  d(qf, w) by induction on the length of w.
• Basis
• Assume
• Then we need to show that
• Dr. Ullmans (Jeffs) slides from CS 154
• http//infolab.stanford.edu/ullman/ialc/jdu-slide
  s.html

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Mutual Induction Proof

• Write up on back of Lecture Overview

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Theorem 2.11 For NFA there is Eq. DFA
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Epsilon (e)-Transitions

• Keyword Searching Example for, format, font

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Epsilon Closure
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Equivalent NFA (without e) for an NFA with e

• Convert NFA with e to an equivalent NFA without e
• Compute transitive closure of e arcs
• If p can reach state q by e arcs and d(r, a)
  contains p (there is a transition from r to q on
  input a) then add q to d(r, a) i.e. add a
  transition from r to q on input a
• xx

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References and Homework

• Ruby pickaxe book Online
• http//whytheluckystiff.net/ruby/pickaxe/
• Authors Website for Text
• http//infolab.stanford.edu/ullman/ialc.html
• Slides, HW, Exams

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Homework

• 2.5.1
• 2.5.3 a,b
• Extra Credit (20pts) Modify dfa1.rb to print all
  strings of lengthlt8 that would be accepted by
  that DFA.

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