Download presentation

Presentation is loading. Please wait.

Published byRudy Jolly Modified over 3 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

CSC 361NFA vs. DFA1. CSC 361NFA vs. DFA2 NFAs vs. DFAs NFAs can be constructed from DFAs using transitions: Called NFA- Suppose M 1 accepts L 1, M 2 accepts.

CSC 361NFA vs. DFA1. CSC 361NFA vs. DFA2 NFAs vs. DFAs NFAs can be constructed from DFAs using transitions: Called NFA- Suppose M 1 accepts L 1, M 2 accepts.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google