Table of Contents
What is the state space for tic-tac-toe?
For tic-tac-toe, a simple upper bound for the size of the state space is 39 = 19,683. (There are three states for each cell and nine cells.) This count includes many illegal positions, such as a position with five crosses and no noughts, or a position in which both players have a row of three.
What is state space search with example?
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 the desired property.
What is a state space search give any example of a game which happens to be a problem of state space search and justify your answer?
So, a set of all possible states for a given problem is known as state space representation of the problem. For example: In chess game: The initial position of all the pieces on a chess board defines the initial state.
How many states are in a tic-tac-toe game?
362,880 possible
There are 362,880 possible move sequences.
What is state space of a problem?
A state space problem P = ( S , A , s , T ) consists of a set of states S, an initial state s ∈ S , a set of goal states T ⊆ S , and a finite set of actions A = { a 1 , … , a n } where each a i : S → S transforms a state into another state. Consider a circular railway track with a siding, as in Figure 1.3.
What should I look for in state-space search?
Explanation: There are four states available in state-space search. They are initial state, actions, goal test and step cost. Become Top Ranker in Artificial Intelligence Now! 6.
Which method is used for state-space search problems?
Explanation: Backward state-space search will find the solution from goal to the action, So it is called as Regression planning.
What is the logic behind tic-tac-toe game?
Each player picks one word in turn and to win, a player must select three words with the same letter. The words may be plotted on a tic-tac-toe grid in such a way that a three-in-a-row line wins. Numerical Tic Tac Toe is a variation invented by the mathematician Ronald Graham. The numbers 1 to 9 are used in this game.
Is the number of possible board states in tic-tac-toe greater than 20000 or not why?
Is the number of possible board states in tic-tac-toe greater than 20,000 or not? Why? Answer: There are nine squares, and for each square there are three possibilities (X, O, or empty). Consequently, the number of possible states is at most 3^9 = 19683 < 20000.
How many different outcomes are there in tic-tac-toe?
255,168 unique games of Tic Tac Toe to be played. Of these, 131,184 are won by the first player, 77,904 are won by the second player, and 46,080 are drawn. This supports the intuition that it is an advantage to begin the game.
What is state space the whole problem?
Explanation: Because state space is mostly concerned with a problem, when you try to solve a problem, we have to design a mathematical structure to the problem, which can only be through variables and parameters. eg. You have given a 4-gallon jug and another 3-gallon jug. Neither has measuring marker on it.
What is state space method?
State space model (SSM) refers to a class of probabilistic graphical model (Koller and Friedman, 2009) that describes the probabilistic dependence between the latent state variable and the observed measurement. The state or the measurement can be either continuous or discrete.
What are the inputs for state-space search?
It takes four arguments: (1) a list of valid starting states, (2) a predicate to decide if we have reached a goal state, (3) a function to generate the successors of a state, and (4) a function that decides in what order to search.
What is the maximum number of Xs which can be placed on a 3by3 tic-tac-toe board without a three in a row in any direction A 4 B 5 C 6 D 7?
Hence, a maximum of 6 Xs can be placed onboard without repeating three-in-a-row in any direction.
What is the heuristic function for the game tic tac toe?
For example, a heuristic function that can be used for the game tic-tac-toe : h (n) = x (n) – o (n) where x (n) is the total of MAX’s possible winning lines (we assume MAX is playing x); o (n) is the total of the opponent’s, i.e. MIN’s winning lines and h (n) is the total evaluation for a state n.
What is state space representation of a problem?
So we can say that to do a search process we need the following. So, a set of all possible states for a given problem is known as state space representation of the problem. For example: In chess game: The initial position of all the pieces on a chess board defines the initial state.
What are the heuristics used in state space representation?
21. State Space Representation and Search Page 21 Figure 12.1 The heuristic used for h (n) is the number of tiles out of place. The numbers next to the letters represent the heuristic value associated with that particular state. 13. The A* Algorithm Search algorithms that are guaranteed to find the shortest path are called admissible algorithms.
What are the operators in a state space representation?
For example, the operators in a state space representation of the 8-puzzle problem are left, right, up and down. < One or more goal states. • The number of operators are problem dependant and specific to a particular state space representation.