An outline of the content sections of the thesis.

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Chapter: Games and Strategies -

Section: Decision Trees - A decision tree is a graph representation of a
strategy.

Section: The Process of Converting Strategies into Boolean Formulas - From our
game theoretic definitions, we develop a method for converting strategies into
Boolean formulas.

Subsection: Resolvable Conflict - A resolvable conflict occurs when the
introduction of an input triggers two output function disjuncts that arose
from decision tree edges from different levels in the tree.

Subsection: Unresolvable conflict - An unresolvable conflict occurs when the
introduction of an input triggers two output function disjuncts that arose
from decision tree edges on the same level of the tree.

Subsection: Move Hiding - All of the chemical reactions we are using to
simulate Boolean functions are monotonic. As such, we can disregard the fact
that (as time passes) a function may evaluate to false after evaluating to
true.

Section: Feasibility - From our definitions of move hiding and conflict, we
develop an idea about what types of Boolean functions we can simulate using
our chemical computation paradigm.

Section: Favorability - A strategy is said to be favorable if it admits only
favorable outcomes for the player using it.

Section: Tic-tac-toe - In the basis of the ideas of the last section, we
analyze the game of tic-tac-toe.

Subsection: Decision Tree Description - All decision trees for the game of
tic-tac-toe adhere to the same basic shape.

Subsection: The Number of Strategies - There are ______ strategies for the
game of tic-tac-toe.

Subsubsection: Labelling Argument - We can obtain an upper bound on the number
of tic-tac-toe strategies by thinking of the problem of coming up with a
strategy as a problem of applying labels to the branches of a tree.

Subsubsection: The Number - There are _______ strategies for the game of
tic-tac-toe.

Subsection: The Number of Favorable Strategies - There are ________ favorable
strategies for the game of tic-tac-toe.

Subsection: The Number of Feasible Strategies - There are ________ feasible
strategies for the game of tic-tac-toe.

Subsection: The Number of Feasible, Favorable Strategies - There are ________
feasible, favorable strategies for the game of tic-tac-toe.

Subsection: Design and Implementation of Tools - From ideas developed in this
and previous sections, we designed and implemented tools to aid us in our
understanding of strategies for the game of tic-tac-toe.

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Chapter: Boolean Formula Manipulation -  

Section: Boolean Minimization - By definition, a Boolean function is minimized
if it meets one of three criteria among all equivalent forms of the function: 
it has a minimal number of disjuncts, it has a minimal number of literals, or
its largest disjunct is of minimal size.

Subsection: Computational Complexity - The problem of Boolean minimization is
in the complexity class Pi_2(p).

Subsection: Methods - The Quine-McClusky algorithm is the hallmark minimization
method. Karnaugh maps can be described as graphical representation of the 
Quine-McClusky algorithm.

Subsection: Implementations - There exist many implementations of Boolean 
formula minimizers.

Section: Our Tools - 

Subsection: Motivation for New Tools - From our descriptions of the problem at
hand, we explain why the current tools are insufficient.

Subsection: Minimo - We have developed a brute force Boolean manipulation
algorithm and implemented it in Java.

Section: Results - From data gathered in the "formula generation" phase, we
used our techniques to attain some noteworthy results.
