Formal Language & Automata Theory

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Presentation transcript:

Formal Language & Automata Theory Shyamanta M Hazarika Computer Sc. & Engineering Tezpur University http://www.tezu.ernet.in/~smh

Regular Languages Regular languages are closed under: Union Concatenation Star operation

Regular Languages Namely, for regular languages and : Union Concatenation Star operation Regular Languages

We will prove Regular languages are closed under: Complement Intersection

We will prove Namely, for regular languages and : Complement Regular Intersection Regular Languages

Complement Theorem: For regular language the complement is regular

Complement Theorem: For regular language the complement is regular Proof: Take DFA that accepts and make nonfinal states final final states nonfinal Resulting DFA accepts

Example

Intersection Theorem: For regular languages and the intersection is regular

Intersection Theorem: For regular languages and the intersection is regular Proof: Apply DeMorgan’s Law:

Intersection regular regular regular regular regular

Standard Representations of Regular Languages DFAs Regular Grammars NFAs Regular Expressions