state space representation
State Space Representation Introduced
- 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 ki S_{ki}Sk iWhen they are all given definite values , a specific state is obtained.
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 .
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 .
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 .
State space method to represent the steps of the problem
The steps of state-space method to represent the problem are as follows
- Defines the description form of the state .
- 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 .
- Defines a set of operators . It makes use of this set of operators to transform the problem from one state to another.
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:
- apply the applicable operator to the initial state to produce a new state;
- Then apply some applicable operators to the new state , and so on, until the resulting state is the target state ;
- 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