September 7

September 7 - goes from every state to every other state...

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CSCI 2670 Introduction to Theory of Computing September 7, 2005

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Agenda Yesterday 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 Proving a language is not regular
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) 1. Except for the start and accept states, one arrow

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Unformatted text preview: goes from every state to every other state and also from each state to itself 2. 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 q ’ q ’ a a a a q q q a ∪ a a a These two portions of GNFA’s recognize the same strings Accounting for loops a ∪ a a a q ’ q ’ a a a a a a a a q q q a a ∪ a a a a ∪ a a a a ∪ a a a...
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September 7 - goes from every state to every other state...

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