September 7

September 7 - state to every other state and also from each state to itself 5 Instead of being labeled with symbols from the alphabet transitions

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CSCI 2670 Introduction to Theory of Computing September 7, 2005
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Agenda •Yester day – Proved every RE has a corresponding DFA • I.e., every RE describes a regular language – Showed how to convert GNFA to RE •Today – Prove every DFA has a corresponding RE – Example of conversion from GNFA to RE • Tomorrow
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GNFA’s A GNFA is an NFA with the following properties: 1. The start state has transition arrows going to every other state, but no arrows coming in from any other state 2. There is exactly one accept state and there is an arrow from every other state to this state, but no arrows to any other state from the accept state 3. The start state is not the accept state
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GNFA’s (continued) 4. Except for the start and accept states, one arrow goes from every
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Unformatted text preview: state to every other state and also from each state to itself 5. Instead of being labeled with symbols from the alphabet, transitions are labeled with regular expressions Converting a GNFA to a RE • If the GNFA has two states, then the label connecting the states is the RE • Otherwise, remove one state at a time without changing the language accepted by the machine until the GNFA has two states Removing one state from a GNFA a 13 a 32 a 12 a 33 q 2 q 1 q 3 q 1 ’ q 2 ’ a 12 ∪ a 13 a 33 * a 32 These two portions of GNFA’s recognize the same strings Accounting for loops a 11 ∪ a 13 a 33 * a 31 q 1 ’ q 2 ’ a 31 a 13 a 32 a 23 a 21 a 12 a 33 a 22 q 2 q 1 q 3 a 11 a 22 ∪ a 23 a 33 * a 32 a 21 ∪ a 23 a 33 * a 31 a 12 ∪ a 13 a 33 * a 32...
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This note was uploaded on 02/07/2011 for the course CS 501 taught by Professor Sm during the Spring '11 term at Indiana.

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September 7 - state to every other state and also from each state to itself 5 Instead of being labeled with symbols from the alphabet transitions

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