Prove that upside-down regular expressions without complement operation cannot describe all regular languages. **You can prove this by finding a regular language and showing that an upside-down RE cannot describe it. You can pick a finite language, then show that if there is an upside-down RE that describes it then the language must contain some extra elements. For the last part, you can make a proof by induction over the RE.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Prove that upside-down regular expressions
without complement operation cannot
describe all regular languages. **You can prove
this by finding a regular language and showing
that an upside-down RE cannot describe it. You
can pick a finite language, then show that if
there is an upside-down RE that describes it
then the language must contain some extra
elements. For the last part, you can make a
proof by induction over the RE.
Transcribed Image Text:Prove that upside-down regular expressions without complement operation cannot describe all regular languages. **You can prove this by finding a regular language and showing that an upside-down RE cannot describe it. You can pick a finite language, then show that if there is an upside-down RE that describes it then the language must contain some extra elements. For the last part, you can make a proof by induction over the RE.
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