# lec04 - Equivalence of DFA and Regular Expressions CSCI...

• Notes
• 25

This preview shows pages 1–10. Sign up to view the full content.

1/19 Equivalence of DFA and Regular Expressions CSCI 3130 Formal Languages and Automata Theory Siu On CHAN Chinese University of Hong Kong Fall 2015

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

2/19 Three ways of doing it [ = { Σ * | ends in 01 } Σ = { 0 , 1 } z 0 z 1 z 2 1 0 0 1 0 1 z 0 z 1 z 2 0,1 0 1 ( 0 + 1 ) * 01 DFA NFA regular expressions
3/19 They are equally powerful DFA NFA regular expressions regular languages

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

4/19 Roadmap regular expressions NFA NFA without ε DFA 3 3
5/19 Examples: regular expression NFA ~ 1 = 0 z 0 z 1 0 ~ 2 = 01 z 0 z 1 z 2 0 1

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

6/19 Examples: regular expression NFA ~ 3 = 0 + 01 NFA 3 z 0 z 1 z 2 z 2 z 3 z 4 z 5 z 6 ε 0 ε ε 0 1 ε ~ 4 = ( 0 + 01 ) * z 0 0 NFA 3 z 0 1 ε ε ε ε
7/19 Regular expressions In general, how do we convert a regular expression to an NFA? A regular expression over Σ is an expression formed by the following rules I The symbols and ε are regular expressions I Every a in Σ is a regular expression I If ~ asd ¢ are regular expressions, so are ~ + ¢ , and ~ *

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

8/19 General method regular expression S NFA z 0 ε z 0 a Σ z 0 z 1 a
9/19 General method regular expression S

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

This is the end of the preview. Sign up to access the rest of the document.
• Fall '15
• SIUON
• Formal language, Regular expression, Nondeterministic finite state machine

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern