Editing Sokoban (section)

==Scientific research==
''Sokoban'' has been studied using the theory of [[Computational complexity theory|computational complexity]]. The computational problem of solving ''Sokoban'' puzzles was first shown to be [[NP-hardness|NP-hard]].<ref>{{cite journal |author1=Michael Fryers |author2=Michael Greene |title= Sokoban |journal=Eureka |issue=54 |year=1995 |pages=25–32 
|url=https://www.archim.org.uk/eureka/archive/Eureka-54.pdf#page=28 |archive-url=https://web.archive.org/web/20240905040633/https://www.archim.org.uk/eureka/archive/Eureka-54.pdf#page=28 |archive-date=2024-09-05}}</ref><ref>{{cite journal |author1=Dorit Dor |author1-link= Dorit Dor |author2=Uri Zwick |author2-link=Uri Zwick |title=SOKOBAN and other motion planning problems |journal=[[Computational Geometry (journal)|Computational Geometry]] |volume=13 |issue=4 |year=1999 |pages=215–228 |doi=10.1016/S0925-7721(99)00017-6 |doi-access=free}}</ref> Further work proved it is also [[PSPACE-complete]].<ref>{{cite journal |author=Joseph C. Culberson |title=Sokoban is PSPACE-complete |journal=Technical Report TR 97-02, Dept. Of Computing Science, University of Alberta |year=1997 |url=http://cl-informatik.uibk.ac.at/teaching/ss07/alth/material/culberson97sokoban.pdf}}</ref><ref>{{cite thesis |author=Robert Aubrey Hearn |title=Games, Puzzles, and Computation |degree=PhD |pages=98–100 |publisher=Massachusetts Institute of Technology |year=2006 |url=https://erikdemaine.org/theses/bhearn.pdf#page=98}}</ref>

Solving non-trivial ''Sokoban'' puzzles is difficult for computers because of the high [[branching factor]] (many legal pushes at each turn) and the large [[Graph traversal|search depth]] (many pushes needed to reach a solution).<ref>{{cite journal |author1=Andreas Junghanns |author2=Jonathan Schaeffer |title=Sokoban: Improving the Search with Relevance Cuts |journal=Theoretical Computer Science |date=2001 |volume=252 |issue=1–2 |url=https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/tcs.pdf#page=5 |page=5 |doi=10.1016/S0304-3975(00)00080-3 |doi-access=free}}</ref><ref>{{cite web |author=Yaron Shoham |title=FESS Draft |page=3 |year=2020 |url=https://festival-solver.site/wp-content/uploads/2020/08/FESS_draft.pdf#page=3}}</ref> Even small puzzles can require lengthy solutions.<ref>{{cite web |author1=David Holland |author2=Yaron Shoham |title=Theoretical analysis on Picokosmos 17 |url=http://membres.lycos.fr/nabokos/analysis.html |archive-url=https://web.archive.org/web/20160607071224/http://www.abelmartin.com/rj/sokobanJS/sokoban-jd.blogspot/sokoban_lessons/picokosmos17/analysis.htm |archive-date=2016-06-07}}</ref>

The ''Sokoban'' game provides a challenging testbed for developing and evaluating [[automated planning|planning]] techniques.<ref>{{cite thesis |author=Timo Virkkala |title=Solving Sokoban |degree=MSc |page=1 |publisher=University of Helsinki |year=2011 |url=https://weetu.net/Timo-Virkkala-Solving-Sokoban-Masters-Thesis.pdf#page=5}}</ref> The first documented automated solver, Rolling Stone, was developed at the [[University of Alberta]]. It employed a conventional search algorithm enhanced with domain-specific techniques such as deadlock detection.<ref>{{cite thesis |author=Andreas Junghanns |title=Pushing the Limits: New Developments in Single-Agent Search |degree=PhD |publisher=University of Alberta |year=1999 |url=https://www.researchgate.net/publication/2305703 |doi=10.7939/R3W95103S |doi-access=free}}</ref><ref>{{cite journal |author1=Andreas Junghanns |author2=Jonathan Schaeffer |title=Sokoban: Enhancing general single-agent search methods using domain knowledge |journal=Artificial Intelligence |volume=129 |issue=1–2 |year=2001 |pages=219–251 |doi=10.1016/S0004-3702(01)00109-6 |doi-access=free}}</ref> A later solver, Festival, introduced the FESS search algorithm and became the first automatic system to solve all 90 puzzles in the widely used XSokoban test suite.<ref>{{cite conference |author1=Yaron Shoham |author2=Jonathan Shaeffer |title=The FESS Algorithm: A Feature Based Approach to Single-Agent Search |date=2020 |url=https://ieee-cog.org/2020/papers/paper_44.pdf |conference=2020 IEEE Conference on Games (CoG) |location=Osaka, Japan |doi=10.1109/CoG47356.2020.9231929 |publisher=IEEE}}</ref><ref>{{cite web |author=Yaron Shoham |title=FESS presentation at the CoG conference (17.5 minutes) |url=https://archive.org/details/fess-algorithm |website=archive.org |language=en |format=video |date=2020}}</ref> Despite these advances, even the most sophisticated solvers cannot solve many highly complex puzzles that humans can solve with time and effort, using their ability to plan ahead, recognize patterns, and reason about long-term consequences.<ref>{{cite web |url=https://archive.org/download/lets-logic-bots-statistics/lets-logic-bots-statistics-2024-oct-06.pdf |title=Let's Logic Bots Statistics |access-date=6 October 2024}}</ref><ref>{{cite web |url=https://sokoban-solver-statistics.sourceforge.io/statistics/LargeTestSuite/ |title=Sokoban Solver Statistics - Large Test Suite |access-date=14 April 2024}}</ref>