Regular expression and its closure properties

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  Regular Expression and its Closure Properties. So far we have seen different ways of specifying regular language: DFA, NFA, ε-NFA, regular expressions and regular grammar. We noted that all these different expressions are equal in power by showing the equivalences. Regular expressions and grammars are considered as generators of regular language while the machines (DFA, NFA, ε-NFA) are considered as acceptors of the language. Now we will look at the properties of regular language. The properties can be broadly classified as two parts: (A) Closure properties and (B) Decision properties (A) Closure Properties 1. Complementation If a language L is regular its complement L' is regular. Let DFA(L) denote the DFA for the language L. Modify the DFA as follows to obtain DFA(L'). Change the final states to non-final states. Change the non-final states to final states. Since there exists a DFA(L') now, L' is regular. This can be shown by an example using a DFA. Let L denote the...