Artificial Intelligence - State Space Representation

State Space Representation Introduced

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• State space representation is a method to represent the problem and its search process in the form of " state space " .
• State-space representation is the most basic formalization method in artificial intelligence , and it is the basis of discussing problem-solving techniques.

Formation of the problem state space

state

• A data structure representing the state of the problem at different moments during the problem solving process .
• Generally, it is represented by an ordered set of variables , which can be formally expressed as: S k = { S k 0 , S k 1 , … , S kn } ( i = 0 , 1 , 2 , … , n ) S_{k } = \lbrace{S_{k0}, S_{k1}, …, S_{kn}}\rbrace(i=0,1,2,…,n)Sk​={ Sk0​,Sk 1,…,Skn​}(i=0,1,2,…,n) 。
• When for each component $S_k$When they are all given definite values , a specific state is obtained.

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operator

• An operation that causes some variable in a state to change , thereby changing the problem from one state to another ;
• It can be divided into steps , processes , rules , mathematical operators , operation symbols or logic symbols , etc.
• For example: in a production system, each production rule is an operator; and in a chess program, an operator is a move .

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state space

• State space : the set of all states of a problemand all available operators .
• A triple is often expressed as: (S, F, G) , where S is the set of all initial states of the problem ; F is the set of operators ; G is the set of target states .
• The state space can also be represented by a directed graph , which is called a state space graph . In a state-space graph, nodes represent states of the problem , and directed edges represent operators .

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solution to the problem

• Starting from the initial state set S of the problem, after a series of operator operations , the target state is reached .
• The sequence of operators used from the initial state to the target state constitutes a solution to the problem.
• The angle of the graph: a path from the initial state to the goal state .

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State space method to represent the steps of the problem

The steps of state-space method to represent the problem are as follows

1. Defines the description form of the state .
2. Use the defined state description form to express all possible states of the problem, and determine the initial state set description and target state set description of the problem .
3. Defines a set of operators . It makes use of this set of operators to transform the problem from one state to another.

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The process of solving problems using state space

The problem-solving process is the process of continuously applying operators to the state , which can be specifically described as:

1. apply the applicable operator to the initial state to produce a new state;
2. Then apply some applicable operators to the new state , and so on, until the resulting state is the target state ;
3. A sequence of operators from the initial state to the goal state is a solution to the problem.

Note: 1. Optimal solution problem 2. Search strategy problem

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Examples of Problem Solving Using State-Space Representation

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A Brief Summary of State-Space Representation

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