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In the introduction, we saw that it's
possible to think of the

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dynamics of the game as a state grpah,
like the one shown here.

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The game is characterized by a finitie
number of states and also

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a finite number of players and there's a
finite number of actions for each player.

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At each point in time the graph is in one
of the possible states.

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The players choose from their possible
actions and

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as the players perform their chosen
actions

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the game changes from one state to
another.

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In the vast majority of games, states and
actions, however, are not monolithic.

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They can be defined in terms of more
fundamental entities.

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In chess, for example, states can be
thought of

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in terms of locations of individual pieces
on the chessboard.

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For example, the state shown on the left
here can be thought of in terms of

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the locations of the white king, the white

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queen, the black king, and the black
queen.

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Also, in the vast majority of games, the
effects of individual actions are local.

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As actions are performed, some of these

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conditions become true and others become
false.

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However the truth values of the majority
of these conditions remain the same.

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The ideas of state decomposition and
limited influence of actions suggest

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the conceptualization of games in terms of
individual propositions and actions

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rather than states, together with the
representation of the effects of

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these actions on these propositions rather
than on the entire states.

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Results is an alternative representation
of dynamics called a Propositional Net.

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Unlike a state

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machine, in which the nodes represent
states,

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in a Propositional Net, the nodes denote

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propositions and actions together with
connectives that

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capture their behavior, as we shall see.

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One of the benefits of formalizing games'
propositional nets is compactness.

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A set of end propositions corresponds to a
set of 2 to the n

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00:02:13,060 --> 00:02:15,550
possible states, all of the different
combinations

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00:02:15,550 --> 00:02:17,610
of the truth values for the n
propositions.

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Thus it's often possible to characterize
the dynamics of games

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with graphs that are much smaller than the
corresponding state machines.

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For example, a prop net with just three
propositions corresponds

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to a state machine with eight possible
states.

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The second benefit of propositional nets
is ease of analysis.

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00:02:37,785 --> 00:02:45,520
It's sometimes possible to use a prop net
to discover independence, or game factors,

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dead states, and other features that can

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dramatically reduce the cost of game tree
search.

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In the next segment, we formalize
propositional nets.

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And in the section thereafter, we show how
to describe games in this way.

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And in the segment after that, we see how
to play

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games using game descriptions encoded as
propositional nets rather than in GDL.

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And we then see how to use propositional

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nets in restructuring games and
discovering game-specific heuristics.