Question

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Explain briefly (2 or 3 sentences) the difference between state space search and game tree evaluation

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Describe these problems, where each one is best solved by a different technique from the following list. Uninformed Search, A* search and Minimax.
Each problem should be described in two-three sentences each.

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For artificial intelligence, computer science

Answer 1

state space search and game tree evaluation

State space search is a process used in the field of computer science, including artificial intelligence (AI), in which successive configurations or states of an instance are considered, with the intention of finding a goal state with a desired property.

A search algorithm is applied to a state space representation to find a solution path. Each search algorithm applies a particular search strategy. If states in the solution space can be revisited more than once a directed graph is used to represent the solution space.

We can define a rooted tree (the "game tree") in which the nodes correspond to game positions, and the children of a node are the positions that can be reached from it in one move

Both a state space and a game tree consist of states connected by operators. However, in a state space, all operators are actions of the problem solver, while in a game tree, operators alternate between actions of the player and actions of the adversary. Therefore, in state space search it suffices to find a goal state (or a path to a goal state), while in game-tree evaluation, one must show that there is an action of the player such that for any action of the adversary there is an action of the player.. ending in a win for the player.

Uninformed Search:

An uninformed search algorithm generates the search tree without using any domain specific knowledge. The two basic approaches differ as to whether you check for a goal when a node is generated or when it is expanded.

A* search

A* serach is a computer algorithm that is widely used in path finding and graph traversal, which is the process of finding a path between multiple points, called "nodes". It enjoys widespread use due to its performance and accuracy. However, in practical travel-routing systems, it is generally outperformed by algorithms which can pre-process the graph to attain better performance.

Explanation
Consider a square grid having many obstacles and we are given a starting cell and a target cell. We want to reach the target cell (if possible) from the starting cell as quickly as possible. Here A* Search Algorithm comes to the rescue.

What A* Search Algorithm does is that at each step it picks the node according to a value-‘f’ which is a parameter equal to the sum of two other parameters – ‘g’ and ‘h’. At each step it picks the node/cell having the lowest ‘f’, and process that node/cell.

We define ‘g’ and ‘h’ as simply as possible below

g = the movement cost to move from the starting point to a given square on the grid, following the path generated to get there.
h = the estimated movement cost to move from that given square on the grid to the final destination.

Minimax

Minimax is a kind of backtracking algorithm that is used in decision making and game theory to find the optimal move for a player, assuming that your opponent also plays optimally. It is widely used in two player turn-based games such as Tic-Tac-Toe, Backgammon, Mancala, Chess, etc.

In Minimax the two players are called maximizer and minimizer. The maximizer tries to get the highest score possible while the minimizer tries to do the opposite and get the lowest score possible.

Every board state has a value associated with it. In a given state if the maximizer has upper hand then, the score of the board will tend to be some positive value. If the minimizer has the upper hand in that board state then it will tend to be some negative value. The values of the board are calculated by some heuristics which are unique for every type of game.

Example:
Consider a game which has 4 final states and paths to reach final state are from root to 4 leaves of a perfect binary tree as shown below. Assume you are the maximizing player and you get the first chance to move, i.e., you are at the root and your opponent at next level. Which move you would make as a maximizing player considering that your opponent also plays optimally

Since this is a backtracking based algorithm, it tries all possible moves, then backtracks and makes a decision.

• Maximizer goes LEFT: It is now the minimizers turn. The minimizer now has a choice between 3 and 5. Being the minimizer it will definitely choose the least among both, that is 3
• Maximizer goes RIGHT: It is now the minimizers turn. The minimizer now has a choice between 2 and 9. He will choose 2 as it is the least among the two values.

Being the maximizer you would choose the larger value that is 3. Hence the optimal move for the maximizer is to go LEFT and the optimal value is 3.

The above tree shows two possible scores when maximizer makes left and right moves.