Regular expressions
Define the term Regular expressions ?
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R is a regular expression if R is– a, for some a ∈Σ– ε, the empty string– Ø, the empty set– (R1 ∪ R2), where R1 and R2 are reg. exprs.– (R1° R2), where R1 and R2 are reg. exprs.– (R1*), where R1 is a regular expression
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Let α be a regular expression of length n. (a) Using procedures shown in class, if we convert α into a regular expression β such that L(β) = L(α). How long β might be? Give a reasonably tight upper bound.
Let REGEXP be the language of valid regular expressions over {a, b}. That is, REGEXP is the set of all strings over the symbols Σ= {a, b, (,), U,*, ^} that are valid regular expressions. For example, the string “a (a U b)" is in REGEXP, whereas the string
Describe the theorem that a language L is recognized by a DFA if and only if L is illustrated by a regular expression.
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Proof the theorem that the class of regular languages is closed under union; that is, if L1 is recognized by a NFA and L2 is recognized by a NFA, then L1 υ L2 is recognized by a NFA as well.
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