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A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string over the alphabet. A string that consists of a sequence a1, a2, . . . , an of symbols will be denoted by the juxtaposition a1a2 an. Strings that have zero symbols, called empty strings, will be denoted by .
{0, 1} is a binary alphabet, and {1} is a unary alphabet. 11 is a binary string over the alphabet {0, 1}, and a unary string over the alphabet {1}.
11 is a string of length 2, |ε| = 0, and |01| + |1| = 3.
Example-The string consisting of a sequence αβ followed by a sequence β is denoted αβ. The string αβ is called the concatenation of α and β. The notation αi is used for the string obtained by concatenating i copies of the string α.
The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations
S-->AAA|B A-->aA|B B-->epsilon
State & prove pumping lemma for regular set. Show that for the language L={ap |p is a prime} is not regular
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Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
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The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular
The Recognition Problem for a class of languages is the question of whether a given string is a member of a given language. An instance consists of a string and a (?nite) speci?cat
1. Does above all''s properties can be used to prove a language regular? 2..which of the properties can be used to prove a language regular and which of these not? 3..Identify one
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