Download

Equivalence and Minimization of Deterministic Finite Automata






Advertisement
Download Presentation
Comments
Mia_John
From:
|  
(3835) |   (0) |   (0)
Views: 440 | Added: 24-10-2011
Rate Presentation: 2 0
Description:
Outline. IntroductionTesting of equivalence of statesDefinitionsTable-filling algorithmMinimization of DFA\'sQuestions. Introduction. Basic Idea of Minimization of DFAsWe can take any DFA and find an equivalent DFA that has the minimum number of states. In fact, this DFA is essentially unique: given any two minimum state DFAs that are equivalent, we can always find a way to rename the states so that the two DFA\' become the same..
Equivalence and Minimization of Deterministic Finite Automat

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use only and may not be sold or licensed nor shared on other sites. SlideServe reserves the right to change this policy at anytime. 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 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -




1. Equivalence and Minimization of Deterministic Finite Automata Joseph Southern CPSC 627 Spring 2003

3. Introduction Basic Idea of Minimization of DFAs We can take any DFA and find an equivalent DFA that has the minimum number of states. In fact, this DFA is essentially unique: given any two minimum state DFAs that are equivalent, we can always find a way to rename the states so that the two DFA? become the same.

4. Introduction Basic Idea Find equivalent states Use table-filling algorithm Partition equivalent states derived from table-filling algorithm into blocks and condense DFA.

5. Definitions Equivalent ? When two distinct states p and q can be replaced by a single state that behaves like both p and q. Distinguishable ? When two states are not equivalent. That is, state p is distinguishable from state q if there is at least one string ? such that one of ?(p,?) and ?(q,?) is accepting, and the other is not accepting.

6. Table-filling Algorithm Initialize all entries as unmarked and with no dependencies. Mark all pairs of a accepting and non-accepting state. For each unmarked pair p,q and input symbol a: Let r = ?(p,a), s = ?(q,a). If (r,s) unmarked, add (p,q) to (r,s)?s dependencies, Otherwise mark (p,q), and recursively mark all dependencies of newly-marked entries.

7. Table-filling Example

25. Minimization of DFA Partition equivalent states together.

28. Citations J. E. Hopcroft, R. Motwani, and J. D. Ullman. "Introduction to Automata Theory, Language, and Computation". Addison--Wesley, 2nd edition, 2001. http://www.cs.yorku.ca/course_archive/2001-02/S/2001B/lectures/gh.pdf

29. Questions?


Other Related Presentations

Copyright © 2014 SlideServe. All rights reserved | Powered By DigitalOfficePro