{\vspace {\baselineskip }}
\contentsline {figure}{\numberline {3.1}{\ignorespaces Path Walking to State 14\relax }}{9}{}%
\contentsline {figure}{\numberline {3.2}{\ignorespaces Color Coding a Small Network Based on Violations\relax }}{10}{}%
\contentsline {figure}{\numberline {4.1}{\ignorespaces A network without Synchronous Firing generating infeasible states\relax }}{18}{}%
\contentsline {figure}{\numberline {4.2}{\ignorespaces Inclusion of Synchronous Firing into GNU Bison, GNU Flex, and the overall program\relax }}{21}{}%
\contentsline {figure}{\numberline {4.3}{\ignorespaces Synchronous Firing in the Graph Generation Process\relax }}{23}{}%
\contentsline {figure}{\numberline {4.4}{\ignorespaces Bar Graph and Line Graph Representations of Synchronous Firing on Runtime\relax }}{26}{}%
\contentsline {figure}{\numberline {4.5}{\ignorespaces Bar Graph and Line Graph Representations of Synchronous Firing on State Space\relax }}{27}{}%
\contentsline {figure}{\numberline {5.1}{\ignorespaces Task Overview of the Attack and Compliance Graph Generation Process\relax }}{30}{}%
\contentsline {figure}{\numberline {5.2}{\ignorespaces Node Allocation for each Task\relax }}{32}{}%
\contentsline {figure}{\numberline {5.3}{\ignorespaces Data Distribution of Task One\relax }}{34}{}%
\contentsline {figure}{\numberline {5.4}{\ignorespaces Communication From Task 1 to Task 2 when the Number of Nodes Allocated is Equal\relax }}{35}{}%
\contentsline {figure}{\numberline {5.5}{\ignorespaces Communication From Task 1 to Task 2 when Task 1 Has More Nodes Allocated\relax }}{36}{}%
\contentsline {figure}{\numberline {5.6}{\ignorespaces Example of a Not Applicable Exploit for the MPI Tasking Testing\relax }}{40}{}%
\contentsline {figure}{\numberline {5.7}{\ignorespaces Speedup and Efficiency of the MPI Tasking Approach for a Varying Number of Compute Nodes with an Increasing Problem Size\relax }}{40}{}%
\contentsline {figure}{\numberline {5.8}{\ignorespaces Example Graph Using the MPI Subgraphing Approach\relax }}{42}{}%
\contentsline {figure}{\numberline {5.9}{\ignorespaces Frontier Merging and Data Distribution Process\relax }}{44}{}%
\contentsline {figure}{\numberline {5.10}{\ignorespaces First iteration results of MPI Subgraphing in terms of Runtime\relax }}{46}{}%
\contentsline {figure}{\numberline {5.11}{\ignorespaces First iteration results of MPI Subgraphing in terms of Speedup and Efficiency\relax }}{47}{}%
\contentsline {figure}{\numberline {5.12}{\ignorespaces Modified Subgraphing Example Graph with Two New Edges\relax }}{49}{}%
\contentsline {figure}{\numberline {5.13}{\ignorespaces Duplicate States Explored vs Actual Number of States for the 1-4 Service Tests\relax }}{50}{}%
\contentsline {figure}{\numberline {5.14}{\ignorespaces Speedup and Efficiency of MPI Subgraphing when using a DHT\relax }}{52}{}%
\contentsline {figure}{\numberline {5.15}{\ignorespaces Runtime of MPI Subgraphing when using a DHT vs not using a DHT\relax }}{53}{}%
\contentsline {figure}{\numberline {6.1}{\ignorespaces Possible Method for Blending MPI and OpenMP for Task 2 of the MPI Tasking Approach\relax }}{56}{}%