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Unformatted text preview: Sep. 15, 2010 (Wednesday) Chapter 1: Regular Languages 7.5 Equivalent Regular Expressions For any finite automaton, there is an equivalent regular expression describing the same language. We prove it by finding an equivalent regular expression for a finite automaton. Basically, we first convert a finite automaton to a special form of Generalized Nondeterministic Finite Automaton (GNFA), and then get an equivalent regular expression from this GNFA. 7.5.1 Generalized Nondeterministic Finite Automaton (GNFA) A GNFA is very similar to an NFA, except that a label of a GNFA can be a regular expression. The following machine is a GNFA, but not an NFA. We have to read either aba or aa , in order to move from start 0 to state 1. This GNFA accepts all strings with substrings aba or aa . b 1 abaUaa a b a 7.5.2 A Special Form of GNFA A GNFA in the special form meets the following three conditions. The start state has only outgoing transitions, but does not have any incoming/loopback transitions.transitions....
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