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State-space search

From Wikipedia, the free encyclopedia

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.

Problems are often modelled as a state space, a set of states that a problem can be in. The set of states forms a graph where two states are connected if there is an operation that can be performed to transform the first state into the second.

State-space search often differs from traditional computer science search methods because the state space is implicit: the typical state-space graph is much too large to generate and store in memory. Instead, nodes are generated as they are explored, and typically discarded thereafter. A solution to a combinatorial search instance may consist of the goal state itself, or of a path from some initial state to the goal state.

Representation

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In state-space search, a state space is formally represented as a tuple , in which:

  • is the set of all possible states;
  • is the set of possible actions, not related to a particular state but regarding all the state space;
  • is the function that establishes which action is possible to perform in a certain state;
  • is the function that returns the state reached performing action in state ;
  • is the cost of performing an action in state . In many state spaces, is a constant, but this is not always true.

Examples of state-space search algorithms

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According to Poole and Mackworth, the following are uninformed state-space search methods, meaning that they do not have any prior information about the goal's location.[1]

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These methods take the goal's location in the form of a heuristic function.[2] Poole and Mackworth cite the following examples as informed search algorithms:

See also

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References

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  1. ^ Poole, David; Mackworth, Alan. "3.5 Uninformed Search Strategies‣ Chapter 3 Searching for Solutions ‣ Artificial Intelligence: Foundations of Computational Agents, 2nd Edition". artint.info. Retrieved 7 December 2017.
  2. ^ Poole, David; Mackworth, Alan. "3.6 Heuristic Search‣ Chapter 3 Searching for Solutions ‣ Artificial Intelligence: Foundations of Computational Agents, 2nd Edition". artint.info. Retrieved 7 December 2017.
  • Stuart J. Russell and Peter Norvig (1995). Artificial Intelligence: A Modern Approach. Prentice Hall.