World Library  
Flag as Inappropriate
Email this Article

State space

Article Id: WHEBN0000546101
Reproduction Date:

Title: State space  
Author: World Heritage Encyclopedia
Language: English
Subject: Markov chain, State space planning, State space search, M/M/1 queue, M/M/∞ queue
Collection: Dynamical Systems, Models of Computation
Publisher: World Heritage Encyclopedia
Publication
Date:
 

State space

In the theory of discrete dynamical systems, a state space is the set of values which a process can take. For example, a system in queueing theory recording the number of customers in a line would have state space {0, 1, 2, 3, ...}. State space is conceptually similar to phase space, but for discrete rather than continuous dynamical systems.

In a computer program, when the effective state space is small compared to all reachable states, this is referred to as clumping. Software such as LURCH analyzes such situations.

In games, the state space is the set of all possible configurations within the game. For instance, in backgammon, it consists of all the possible positions in which the 30 pieces can be placed, whether on the board, on the bar or in the bear-off tray. Within this state space there is the subset of positions which are valid according to the rules of backgammon. A game's total state space is often readily calculated whereas finding the subset of valid positions may be a considerable challenge. For example, a Chess board has 8x8=64 positions, and there are 32 distinct pieces, so the total state space has \tbinom{64}{32} = 1,832,624,140,942,590,534 states.[1] However, most of those states are not valid positions.[2] The size of a game's state space is related to its complexity.

State space search explores a state space.

See also

References

  1. ^ Chess.com http://www.chess.com/learn-how-to-play-chess. Retrieved 31 December 2014. 
  2. ^ Hamkins, Joel. MathOverflow http://mathoverflow.net/a/138499. Retrieved 31 December 2014. 
  • Equivalence Relations on Finite Dynamical Systems, Laubenbacher, R. Pareigis, B., ADVANCES IN APPLIED MATHEMATICS, 2001, VOL 26; PART 3, pages 237–251
  • State-space search: algorithms, complexity, extensions, and applications, Weixiong Zhang, Springer, 1999, ISBN 978-0-387-98832-0
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.