The function that associates a language to each regular expression over an alphabet is defined recursively. The base for the definition is the statement that _______ , _______ , and _______ for every a in . The recursion for the definition specifies that if and are the languages defined by the regular expressions r and r’ over , then _______ , _______ , and _______ .
To fill in the blanks of the statement on languages and regular expression.
“ The function that associated a language to each regular expression over an alphabet is defined recursively. The base for the definition is the statement that for every in . The recursion for the definition specifies that if and are languages defined by the regular expressions over , then ”.
The language and regular expressions are defined on an alphabet .
By the notation , we denote language that is formed by a set of string defined on a particular alphabet . A language is always a set of strings.
Also, the notation is used to denote the null set.
Then, a language defined by null set has only the strings formed by null set. Hence it has no strings actually, Therefore, the language defined by a null set is also a null set.
Also, the notation is used to denote a string with zero length, (a string has no characters). Hence, the language defined by contains set of strings of zero length.
When is a string defined on alphabet , the language defined by has only one string .
Until is a regular expression defined on , denotes the concatenation of two regular expressions. Hence, is the language of that concatenated two regular expressions. Therefore, concatenates the languages defined by and
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