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@@ -9,6 +9,7 @@
 \usepackage[english]{babel}
 \usepackage{fancyhdr}
 \usepackage{titling}
+\usepackage{hyperref}
 \renewcommand{\thesection}{Exercise \Alph{section}:}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -65,7 +66,75 @@ Our group consists of the following members:
 \end{center}
 
 \section{Finding invalid blocks}
-% Fill here your answers for exercise A 
+
+For this exercise all invalid blocks contained in the database provided to us
+had to be found. While there is an
+official\footnote{\url{https://en.bitcoin.it/wiki/Protocol\_rules\#.22block.22\_messages}}
+algorithm which allows network participants to verify whether a block is invalid
+or not, the stripped-down version of the blockchain we received does not require
+all the steps. This stripped-down version of the algorithm thus specifies which
+constraints the data must satisfy:
+
+\begin{enumerate}
+    \item All blocks which do not have the coinbase transaction as their first
+        transaction are invalid. This will be achieved by creating a view which
+        lists all coinbase transactions. Then we query the database for all
+        first transactions of each block and check if that transaction is in the
+        view of all coinbase transactions. If it is not, we reject the block and
+        add it to the invalid list.
+    \item All blocks which contain transactions which do not have inputs or
+        outputs are invalid. We split this task into two queries, one for
+        checking if a block contains transactions with zero inputs and another
+        one for checking if a block contains transactions with zero outputs.
+    \item All blocks which have transactions with an invalid output value or
+        where the sum of all output values exceeds the legal money range are
+        invalid. This task is split into two queries as well. One for checking
+        if individual output values are outside of the legal money range and a
+        second one for checking if the sum of all output values per transaction
+        is outside of the legal money range.
+    \item Reject all blocks which have transactions with inputs that do not have
+        a corresponding output. For this task we first create a view which finds
+        all non coinbase transactions. The output of that query is then filtered
+        for all inputs which are not part of a coinbase transaction (so the non
+        coinbase inputs). Finally, the non coinbase inputs are joined with the
+        outputs and rows containing \texttt{NULL} as their \texttt{value}
+        indicate an invalid block.
+    \item All blocks which contain transactions where the input's
+        \texttt{sig\_id} field is not the same as the output's \texttt{pk\_id}
+        field are invalid. Since we are not interested in the coinbase
+        transactions, the query uses the non coinbase inputs again to join them
+        with the outputs. If the two fields do not match, the block is invalid.
+    \item All blocks which have inputs for which there exist outputs which have
+        already been spent are invalid. This task is split into three queries.
+        First, we find all outputs which have more than one input. Second, for
+        all the outputs found, we find the corresponding inputs where the output
+        was first spent. Third, the two tables are combined such that blocks
+        with outputs which have corresponding inputs that are not listed as the
+        first spending occurrence, are marked as invalid.
+    \item All blocks containing inputs which are not in the legal money range
+        are invalid. First, we construct a view which gathers all transactions
+        and their corresponding sum of value for all inputs. All blocks
+        containing input sums which are outside of the legal money range are
+        marked as invalid. Second, we reuse the view of all non coinbase inputs
+        and filter them for the ones which have an output value outside of the
+        legal money range.
+    \item All blocks where the sum of input values is smaller than the sum of
+        output values are invalid. This task allows us to reuse the view created
+        earlier of all input sums. Additionally, the sum of output values is
+        obtained similarly to the input sums. After joining both input sums and
+        output sums, we can filter for blocks which have smaller input sums than
+        output sums. Those blocks are invalid.
+    \item All blocks where the coinbase value is larger than the sum of the
+        block creation fee and all transaction fees are invalid. This task is
+        split into four queries. First, we create a view which shows all block
+        ids and their coinbase values. Second, we need to know the sum of all
+        input values per block. Third, we repeat that query for the sum of the
+        output values per block. Lastly, these three tables are joined and all
+        blocks which satisfy the constraint are invalid.
+\end{enumerate}
+
+Finally, the invalid blocks are written to the \texttt{invalid\_blocks} table
+and all duplicates are removed.
 
 \section{UTXOs}
 % Fill here your answers for exercise B