41 lines
1.0 KiB
Markdown
41 lines
1.0 KiB
Markdown
# Pumping Lemma
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Show $L = \{0^n1^n | n=03 \text{ is not regular}\}$.
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Assume $L$ is regular.
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Pick a string and some pumping length, $P$.
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$s=0^p1^p$
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Now show that for any way to divide the string into $xyz$, pumping $s$ results in a string outside of the language.
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$xy^2z$ contains symbols out of order, and more 0s than 1s.
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# Finite State Machine
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A finite automaton is a 5 tuple (Q, $\Sigma$, $\delta$, q, F) where
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1) Q is a finite set called the states
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2) $\Sigma$ is a finite set called the _alphabet_
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3) $\delta = Q \times \Sigma \rightarrow Q$ is the transition function
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4) $q \in Q$ is the start state
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5) $F \subset Q$ is the set of accept state
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# Chomsky Normal Form
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Let $G$ be a Context Free Grammar (CFG). $G$ is in Chomsky Normal Form provided that all rules are of the form
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1) $A \rightarrow AA$
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2) $A \rightarrow u$
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The start state cannot appear on the right hand side. Cannot $A \rightarrow \epsilon$ unless start state.
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# NFA that's the union of two languages
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# Misc.
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$\text{REG} \in \text{CFL}$
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but
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$\text{REG} \neq \text{CFL}$
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