# ch1_6 - Sep 13 2010(Monday Chapter 1 Regular Languages 7...

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Sep. 13, 2010 (Monday) Chapter 1: Regular Languages 7 Regular Expressions In the last class, we showed that the set of languages recognized by DFAs is the same as that recognized by NFAs (i.e. DFAs=NFAs). That is, if a language is recognized by an NFA, it is also regular. In this class, we will study a new way “Regular Expression” (RE) to describe a regular language, and we will show that REs = NFAs = DFAs. Finite Automata Expressions Regular Nondeterministic Finite Autonata Deterministic 7.1 Definition of a regular expression R is a regular expression over an alphabet Σ , if R is regular expressions languages a for some a in Σ { a } ε { ε } {} R 1 R 2 L ( R 1 ) L ( R 2 ) R 1 R 2 = R 1 R 2 L ( R 1 ) L ( R 2 ) R * 1 L ( R 1 ) * where R 1 and R 2 are regular expressions If there are multiple operations in a regular expression, we follow the following order: the star operation the concatenation operation the union operation But if a regular expression has parentheses, then we do the operations in the parentheses first.

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