\chapter{Future Work}

\label{chap:future}

The research which produced this thesis can easily be continued in many
different avenues.

\section{Tic-Tac-Toe}

While there are other versions of tic-tac-toe to be explored, there are
still questions about the original game that remain unanswered.
Among them: how many feasible strategies are there?
Attempts were made at answering this question during the development of this
thesis. None were fruitful enough to merit consideration.

We did, however, find some strategies that map to 
%relatively simple technologies.
disjunctive normal form formulas  with conjunctions of at most five literals.
This makes us wonder
%begs the question 
as to what technologies are sufficient to represent
a strategy for the game of tic-tac-toe (or any other game for that matter).

\section{Other Games}

There are several games whose strategies may be converted to Boolean formulas
using a method similar to that described in this thesis. Among them are
Connect Four and Othello.

\subsection{Connect Four}

Connect Four is a game in which players permanently claim fields as their own
by dropping discs into vertical columns. 
Traditionally the game is played with seven columns (each with a height of 
five fields).
The vertical nature of the columns implies that no player may claim a field
until the field below it has been claimed (with the exception of the fields 
at the bottoms of the columns). 
Connect Four would be an interesting application for our strategy conversion
method.

\subsection{Othello}

Othello is a game in which players select fields but ownership of
fields is not permanent. The ability of the results of this research
to map to the game of Othello is very closely tied to the amount of
``realism'' one wants from the performance of the Boolean formulas.

As the work stands, the claiming of fields is permanent while the
claim is not staked throughout the game.
A perfect simulation of the game of Othello (with field ownership
changes) is well outside the scope of the current abilities of this
technology.