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03-regular-languages-NFA

03-regular-languages-NFA - Regular Languages Denition A...

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Regular Languages Definition: A language is called a regular language if some finite automaton recognizes it – p. 1/2 1

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Regular Operations Definition: Let A and B be regular languages, we define the following operations: Union: A B = { x | x A or x B } . Concatenation: A B = { xy | x A and y B } . Star (Kleene Closure): A * = { x 1 x 2 . . . x k | k 0 and each x i A } . – p. 2/2 1
A B is a Regular Language Theorem: If A 1 and A 2 are regular languages, then so is A B . – p. 3/2 1

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A B is a Regular Language – p. 4/2 1
Nondeterminism Up to now we have only considered machines where, given a state and given an input symbol, the next state is uniquely defined - deterministic machines (DFA) However, we could conceive of machines that, given a state and a particular input symbol, have a choice of states to move to - nondeterministic machines (NFA) We will see that nondeterminism does not add to the power of the NFA to recognize larger sets of languages, but nondeterminism adds to the expressiveness of the machines, i.e., it is much easier to build a nondeterministic machine for a particular regular language than a deterministic machine. – p. 5/2 1

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Example: Let A be the language consisting of all string over Σ = { 0 , 1 } containing a 1 in the third position from the end (e.g. 00100 , 0101 , 1100 A ). DFA:
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• Spring '11
• Staff
• Formal language, Formal languages, Regular expression, Regular language, Pumping lemma for regular languages

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03-regular-languages-NFA - Regular Languages Denition A...

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