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Commit bffd17b3 authored by Theo von Arx's avatar Theo von Arx
Browse files

Add Complexity Classes

parent fdd00857
......@@ -250,6 +250,27 @@ In pseudo code, we would like to have:
Proof, that there exists no such program: Run \texttt{test(test)}. The output of this program is not well defined.
\subsubsection{Komplexitätsklassen $\mathcal{P}$ und $\mathcal{NP}$ }
\begin{fdef}
\begin{itemize}
\item $\mathcal{P}$ is the complexity class containing decision problems which can be solved by a Turing machine in polynomial time.
\item $\mathcal{NP}$ is the class of decision problems solvable by a non-deterministic polynomial time Turing machine such that the machine answers "yes", if at least one computation path accepts, and answers "no", if all computation paths reject.\\
Informally, there is a Turing machine which can check the correctness of an answer in polynomial time.
\end{itemize}
\end{fdef}
\begin{itemize}
\item An important notion is the set of $\mathcal{NP}$-complete decision problems, which is a subset of $\mathcal{NP}$ and might be informally described as the "hardest" problems in $\mathcal{NP}$.
\item If there is a polynomial-time algorithm for even one of them, then there is a polynomial-time algorithm for all the problems in NP.
\item Unsolved question: Is $\mathcal{P=NP}$?
Are there problems which cannot be solved in polynomial time?
\end{itemize}
\subsection{Beispiele - Kontextfreie Grammatiken}
\begin{itemize}
......
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