Download presentation

Presentation is loading. Please wait.

Published byRudy Jolly Modified over 2 years ago

1
Reducing DFA’s Section 2.4

2
Reduction of DFA For any language, there are many DFA’s that accept the language Why would we want to find the smallest? Algorithm: Finds smallest equivalent DFA

3
Distinguishable States A state p is indistinguishable from another q if, for all walks w, δ*(p,w) F implies δ*(q,w) F and δ*(p,w) F implies δ*(q,w) F Otherwise, they are distinguishable

4
Two Step Algorithm First, mark all pairs of states as distinguishable or indistinguishable Then, merge indistinguishable states into one state for the smaller graph

5
Mark Algorithm 1.Remove inaccessible states 2.Mark all states in F as distinguishable from those not in F. 3.Repeat until all pairs are marked: For all pairs (p,q) and all symbols (a), if δ(p,a) is distinguishable from δ(q,a), then p is distinguishable from q.

6
Reduce Algorithm Create a state for each set of indistinguishable states from the Mark algorithm. Rewrite transitions between states. If δ(p,a) = q, then make a transition from the node containing the original p to the node containing the original q and label it a.

7
Example q0 q1 q2 q3 q4 0 0 0 0 0,1 1 1 1 1 01 q0q1q3 q1q2q4 q2q1q4 q3q2q4

8
Example 01 q0q1q3 q1q2q4 q2q1q4 q3q2q4 Distinguishable Pairs Final –Nonfinal states (q0,q4) (q1,q4) (q2,q4) (q3,q4)

9
Example 01 q0q1q3 q1q2q4 q2q1q4 q3q2q4 Distinguishable Pairs: Chart Compare (q0,q4) (q1,q4) (q2,q4) (q3,q4) (q0,q1) (q0,q2) (q0,q3)

10
Example Distinguishable Pairs: (q0,q4) (q1,q4) (q2,q4) (q3,q4) (q0,q1) (q0,q2) (q0,q3) Indistinguishable Pairs: {q0} {q1, q2,q3} {q4}

11
Example q0 q1 q2 q3 q4 0 0 0 0 0,1 1 1 1 1 01,2,34 0,11 0

Similar presentations

OK

1 1 CDT314 FABER Formal Languages, Automata and Models of Computation Lecture 3 School of Innovation, Design and Engineering Mälardalen University 2012.

1 1 CDT314 FABER Formal Languages, Automata and Models of Computation Lecture 3 School of Innovation, Design and Engineering Mälardalen University 2012.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on world war 1 and 2 Ppt on latest technology inventions Download ppt on bermuda triangle Ppt on nuclear power generation Download ppt on energy and environment Ppt on solid dielectrics and waves Ppt on conceptual art images Ppt on condition monitoring techniques Ppt on odisha cultured Ppt on producers consumers and decomposers in the desert