Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

(iv) If all of the nodes connected to CURRENT through the new
marked arcs have been labeled SOLVED, Then mark the
CURRENT SOLVED.
(v) If CURRENT is marked SOLVED or the cost of CURRENT
was changed, Then propagate its new status back up the tree,
add all the ancestors of CURRENT to S.
Until S is empty.
Until INIT is labeled solved or its h’ value becomes greater than a maximum
level called FUTILITY:
End.
4.4 Adversary Search
In this section we will discuss special type of search techniques required in a
game playing between two opponent players. The state space in this case is
represented by a tree or graph and includes the possible turns of both players.
Each level of the search space in the present context denotes the possible turn
of one player only. We start with a simple algorithm called MINMAX and
gradually develop more complex algorithms for game playing.
4.4.1 The MINIMAX Algorithm
The MINIMAX algorithm considers the exhaustive possibility of the state
transitions from a given state and consequently covers the entire space. The
algorithm, thus, is applicable to games having few possible state transitions
from a given trial state. One typical example that can be simulated with
MINIMAX is the NIM game. A NIM game is played between two players.
The game starts with an odd number of match sticks, normally 7 or 9, placed
on a single row, called a pile. Each player in his turn has to break a single
pile into two piles of unequal sticks, greater than zero. The game will come
to an end when either of the two players cannot give a successful move. The
player who cannot give a successful move the first time will lose the game.
According to standard convention we name the two players MINIMIZER
and MAXIMIZER. NIM is a defensive game and consequently the opening
player, here, is called the MINIMIZER. For a game such as tic-tac-toe, where
the opener always gets the benefit, the opening player is called the
MAXIMIZER. A graph space for the NIM game is presented in fig. 4.12 (a),
demarcating MAXIMIZER’s move from the MINIMIZER’s move.