31+Slides--NFAs%2C+Regular+Expressions

31 Slides-NFAs R - CS103 HO#31 Slides-NFAs Regular Expressions 1 Theorem 1.39 Every nondeterministic finite automaton has an equivalent

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CS103 HO#31 Slides--NFAs, Regular Expressions 4/25/11 1 Theorem 1.39 : Every nondeterministic finite automaton has an equivalent deterministic finite automaton. To convert an NFA N = (Q, , , q , F) recognizing A into a DFA M = (Q', , ' , q ', F ' ): 1. Q' = P (Q) 2. For R Q' and a , let ' (R, a) = { q Q | q (r, a) for some r R }. Alternately, we may write ' (R, a) = (r, a) 3. q ' = { q } 4. F' = { R Q' | R contains an accepting state of N } This does not handle -transitions. r R without -transitions. Theorem 1.39 : Every nondeterministic finite automaton has an equivalent deterministic finite automaton. To convert an NFA N = (Q, , , q , F) recognizing A into a DFA M = (Q', , ' , q ', F): 1. Q' = P (Q) 2. For R Q' and a , let ' (R, a) = { q Q | q E( (r, a)) for some r R }. 3. q ' = E({ q }) 4. F' = { R Q' | R contains an accepting state of N } For an NFA with -transitions, make the changes shown in red, where { E(R) = { q Q | q can be reached by following 0 or more -arrows }. Sipser has a good example of the Subset Construction on pp. 57 – 58. For the DFA, Q' = P ({1, 2, 3}), so there are 8 states. A Bad Case for the Subset Construction q q 1 q 2 q n ... 0, 1 0, 1 0, 1 0, 1 1 0, 1 If we build an NFA like this for some value of n, the language accepted is the set of all strings of 0's and 1's such that the n th symbol from the end is a 1. If we build a DFA to accept the same language, it will have to "remember" the last n symbols it has read, and be prepared for any combination of 0's and 1's after the critical 1. Although converting an NFA to a DFA often results in a machine with roughly the same number of states as the NFA, this one needs at least 2 n states....
View Full Document

This note was uploaded on 06/01/2011 for the course EE 103 taught by Professor Plummer during the Spring '11 term at Stanford.

Page1 / 5

31 Slides-NFAs R - CS103 HO#31 Slides-NFAs Regular Expressions 1 Theorem 1.39 Every nondeterministic finite automaton has an equivalent

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online