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\begin{frame}[fragile]{From Context-Sensitive Grammars to LBA's} \begin{goal}{Theorem} For every context-sensitive grammar $G$ there exists an LBA $M$ such that $L(M) = L(G)$. \end{goal} \pause\medskip \begin{proof} A derivation of $w \in L(G)$ contains only words of length $\leq |w|$. \medskip A nondeterministic Turing machine can simulate (guess) this derivation without leaving the bounds of $w$. \end{proof} \end{frame}