# Regular Expressions Three - Automata and Complexity Theory - Lecture Slides, Slides for Automata. Bidhan Chandra Krishi Viswa Vidyalaya

## Automata

Description: Some concept of Automata and Complexity Theory are Administrivia, Closure Properties, Context-Free Grammars, Decision Properties, Deterministic Finite Automata, Intractable Problems, More Undecidable Problems. Main points of this lecture are: Regular Expressions Three, Practical Applications, Mathematics, Phenomenon Discovered, Definitional Power, Regular Languages, Formally Defined, Language, Induction, Regular Language
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Chapter Seven:
Regular Expressions
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The first time a young student sees the mathematical constant , it
looks like just one more school artifact: one more arbitrary symbol
whose definition to memorize for the next test. Later, if he or she
persists, this perception changes. In many branches of mathematics
and with many practical applications, keeps on turning up. "There
it is again!" says the student, thus joining the ranks of
mathematicians for whom mathematics seems less like an artifact
invented and more like a natural phenomenon discovered.
So it is with regular languages. We have seen that DFAs and
NFAs have equal definitional power. It turns out that regular
expressions also have exactly that same definitional power: they can
be used to define all the regular languages, and only the regular
languages. There it is again!
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Outline
7.1 Regular Expressions, Formally Defined
7.2 Regular Expression Examples
7.3 For Every Regular Expression, a Regular
Language
7.4 Regular Expressions and Structural
Induction
7.5 For Every Regular Language, a Regular
Expression
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Concatenation of Languages
The concatenation of two languages L1 and
L2 is L1L2 = {xy | x L1 and y L2}
The set of all strings that can be constructed
by concatenating a string from the first
language with a string from the second
For example, if L1 = {a, b} and L2 = {c, d} then
L1L2 = {ac, ad, bc, bd}
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