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Regular expressions prove - PowerPoint PPT Presentation

Proof . To prove subset relation we need to show that

Theorem 2 . Let A , B and C be sets of strings. Then ( A ? B )? C ? A ? C ? B ? C. Proof . To prove subset relation we need to show that for any string w, w ? ( A ? B )? C ? w ? A ? C ? B ? C. Why not to prove A ? C ? B ? C ? ( A ? B )? C as well?.

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Example. Simplify a regular expression:

Distinct regular expressions may represent the same language: a + b and b + a represent the same language { a , b }. Two expressions R and S that represent the same language, L ( R ) = L ( S ), are considered equal . For example, a + a * = a *

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Regular expressions prove - PowerPoint PPT Presentation

Proof . To prove subset relation we need to show that

Example. Simplify a regular expression: