State Space Search: Fundamentals and Applications

By Fouad Sabry

What Is State Space Search

State space search is a technique that is employed in the field of computer science, particularly artificial intelligence (AI), in which consecutive configurations or states of an instance are explored, with the objective of finding a goal state with the desired feature. The term "state space search" comes from the phrase "state space," which refers to the space in which the process takes place.

How You Will Benefit

(I) Insights, and validations about the following topics:

Chapter 1: State Space Search

Chapter 2: Brute-Force Search

Chapter 3: Heuristic in Computer Science

Chapter 4: Local Search Optimization

Chapter 5: Game Tree

Chapter 6: Constraint Satisfaction Problem

Chapter 7: Adversarial Search

Chapter 8: Markov Decision Process

Chapter 9: Reinforcement Learning

Chapter 10: Combinatorial search

(II) Answering the public top questions about state space search.

(III) Real world examples for the usage of state space search in many fields.

(IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of state space search' technologies.

Who This Book Is For

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of state space search.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: Jun 28, 2023

Book preview

Chapter 1: State space search

State space search is a process that is 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. State space search is also used in the field of artificial intelligence (AI).

Problems are sometimes modeled as state spaces, which are collections of states that a problem may be in at any one time. A graph is created by the set of states, and two states are related to one another in that graph if there is an operation that can be carried out to turn the first state into the second state.

Because the state space is implicit, classic search techniques from the field of computer science do not always apply when doing a state space search. The usual state space graph is far too vast to build and keep in memory because of this. Instead, nodes are created while they are being studied and are often thrown away afterward. A solution to a combinatorial search instance could be the target state itself, or it might be a route from a starting state to the goal state. Either way, a solution is something that can be found.

When searching state spaces, a state space is formally represented as a tuple

{\displaystyle S:\langle S,A,Action(s),Result(s,a),Cost(s,a)\rangle }

, in which:

S is the set of all possible states; A is the set of possible actions, not pertaining to a specific state but rather all states and the state space as a whole; Action(s) is the function that establish which action is possible to perform in a certain state; Result(s,a) is the function that returns the state reached performing action a in state s

Cost(s,a) is the cost of performing an action a in state s .

A is a constant in several different state spaces, However, this is not always the case.

The following are examples of uninformed state-space search strategies, as defined by Poole and Mackworth. This indicates that the methods in question do not have any previous knowledge of the precise location of the target.

Traditional searches that start at the depths

Searching across a wider area initially.

Iterative deepening

a search that prioritizes the lowest cost or one that looks at costs uniformly (UCS)

These techniques make use of heuristic functions to determine where the target should be placed. The following are some cases that Poole and Mackworth mention as examples of informed search algorithms::

depth-first search based on informed or hunches

search that prioritizes profit above quality

A* search

{End Chapter 1}

Chapter 2: Brute-force search

In the field of computer science, a brute-force search, exhaustive search, or generate and test is a very general problem-solving technique and algorithmic paradigm that consists of methodically enumerating all possible candidates for the solution and checking whether or not each candidate satisfies the problem's statement. Other names for this type of search include exhaustive search and brute-force search. Generating and testing solutions is another name for this type of search.

An method that uses brute force to identify the divisors of a natural number n would enumerate all numbers from 1 to n and check to see whether each of them divides n without leaving a remainder. This process would continue until all divisors had been found. The eight queens problem may be solved using a method known as brute force, which involves checking each conceivable arrangement of eight pieces on a chessboard with 64 squares to see whether any of the pieces (queen pieces) can attack any of the other pieces on the board. As a result, a brute-force search is used the majority of the time either when the size of the issue is constrained or when there are problem-specific heuristics that can be utilized to minimize the collection of possible solutions to a size that is more manageable. Additionally, the approach is used in situations in which ease of implementation is prioritized above speed of completion.

This is the case, for example, in crucial applications in which any faults in the algorithm would have extremely catastrophic implications or when using a computer to prove a mathematical theorem. In both of these situations, any mistakes in the method would have very serious repercussions. Searching using brute force may also be beneficial as a baseline approach for comparing the performance of various algorithms or metaheuristics. In point of fact, the term brute-force search may be used to refer to the most basic form of a metaheuristic. Retracing is not to be mistaken with brute force search since with backtracking, enormous sets of potential solutions may be eliminated without first being explicitly listed (as in the textbook computer solution to the eight queens problem above). Linear search is another term for the brute-force approach of locating anything in a database, which involves checking each entry of the table in the order that it was created.

The next possible contender for the position of President is c.

valid (P, c): Determine whether the candidate c in question is a solution for P.

output (P, c): implement the solution c of P in a manner that is suitable for the application.

The subsequent method must also indicate when all of the potential candidates for instance P have been eliminated, after the one before it c.

That may be accomplished quickly and easily by returning a null candidate., some conventional data value Λ that is distinct from any real candidate.

Likewise the first procedure should return Λ if there are no candidates at all for the instance P.

The algorithm then expresses the brute-force approach in its simplest form.

c ← first(P)

while c ≠ Λ do

if valid(P,c) then

output(P, c)

c ← next(P, c)

end while

For example, while trying to find the factors that divide n, an integer, The value of n may