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Motion planning with pull moves [article]

Marcus Ritt
2010 arXiv   pre-print
It is well known that Sokoban is PSPACE-complete (Culberson 1998) and several of its variants are NP-hard (Demaine et al. 2003).  ...  In this paper we prove the NP-hardness of some variants of Sokoban where the warehouse keeper can only pull boxes.  ...  Dor and Zwick [8] show that Sokoban is also PSPACE-complete when the robot can push up to two boxes or pull one box, and the boxes have size 2 × 1.  ... 
arXiv:1008.2952v1 fatcat:xoymwqh4ufcyjbiadtaspuubxu

1 x 1 Rush Hour with Fixed Blocks is PSPACE-complete [article]

Josh Brunner, Lily Chung, Erik D. Demaine, Dylan Hendrickson, Adam Hesterberg, Adam Suhl, Avi Zeff
2020 arXiv   pre-print
We prove that it is PSPACE-complete to decide whether a given block can reach the left edge of the board, by reduction from Nondeterministic Constraint Logic via 2-color oriented Subway Shuffle.  ...  Our result answers a 15-year-old open problem by Tromp and Cilibrasi, and strengthens previous PSPACE-completeness results for Rush Hour with vertical 1 × 2 and horizontal 2 × 1 movable blocks and 4-color  ...  Subway Shuffle is PSPACE-complete.  ... 
arXiv:2003.09914v2 fatcat:rvioeuniwfcdzlkk36sqjhdxoy

1 X 1 Rush Hour with Fixed Blocks Is PSPACE-Complete

Josh Brunner, Lily Chung, Erik D. Demaine, Dylan Hendrickson, Adam Hesterberg, Adam Suhl, Avi Zeff, Ryuhei Uehara, Martin Farach-Colton, Giuseppe Prencipe
2020 Fun with Algorithms  
We prove that it is PSPACE-complete to decide whether a given block can reach the left edge of the board, by reduction from Nondeterministic Constraint Logic via 2-color oriented Subway Shuffle.  ...  Our result answers a 15-year-old open problem by Tromp and Cilibrasi, and strengthens previous PSPACE-completeness results for Rush Hour with vertical 1 × 2 and horizontal 2 × 1 movable blocks and 4-color  ...  Shuffle is PSPACE-complete.  ... 
doi:10.4230/lipics.fun.2021.7 dblp:conf/fun/BrunnerCDHHSZ21 fatcat:xanal3nqszhyleccjmaurumd6i

Playing Games with Algorithms: Algorithmic Combinatorial Game Theory [chapter]

Erik D. Demaine
2001 Lecture Notes in Computer Science  
The purpose of this paper is to provide an overview of the area to encourage further research.  ...  Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer.  ...  It remains open whether Dots-and-Boxes or Strings-and-Coins are in NP or PSPACE-complete from an arbitrary configuration.  ... 
doi:10.1007/3-540-44683-4_3 fatcat:7zoqv6zdwzbdvn34jryyg5etim

On the Complexity of 2-Player Packing Games [article]

Oliver Korten
2019 arXiv   pre-print
We prove that in both games, deciding the outcome under perfect play is PSPACE-complete.  ...  In the second game, there is a fixed sequence of polycubes, and on a player's turn they drop the next piece in through the top of the box, after which it falls until it hits a previously placed piece (  ...  It is PSPACE-complete to determine the winner of a Polycube Packing game from an initially empty N × M × 3 box.  ... 
arXiv:1911.07793v1 fatcat:4zo3ulrdkraabiizrbnsti6qgi

Playing Games with Algorithms: Algorithmic Combinatorial Game Theory [article]

Erik D. Demaine, Robert A. Hearn
2008 arXiv   pre-print
The purpose of this paper is to provide an overview of the area to encourage further research.  ...  Our review of background and survey of algorithmic results are by no means complete, but should serve as a useful primer.  ...  piece per dot that is two-fold rotationally symmetric around the dot.  ... 
arXiv:cs/0106019v2 fatcat:lae3nzasxvbsljdya7bu3t64ou

PSPACE-Completeness of Sliding-Block Puzzles and Other Problems through the Nondeterministic Constraint Logic Model of Computation [article]

Robert A. Hearn, Erik D. Demaine
2004 arXiv   pre-print
Finally, we strengthen the existing result that the pushing-blocks puzzle Sokoban is PSPACE-complete, by showing that it is PSPACE-complete even if no barriers are allowed.  ...  Deciding whether this simple graph model can be manipulated in order to reverse the direction of a particular edge is shown to be PSPACE-complete by a reduction from Quantified Boolean Formulas.  ...  Just as many NP-complete problems become PSPACE-complete when turned into two-player games [9] , it is also natural to expect that they become PSPACE-complete when turned into dynamic puzzles.  ... 
arXiv:cs/0205005v5 fatcat:ozdyozcsgnh3fl2imiknvudany

PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation

Robert A. Hearn, Erik D. Demaine
2005 Theoretical Computer Science  
.], by showing that it is PSPACE-complete even if no barriers are allowed.  ...  Finally, we strengthen the existing result that the pushing-blocks puzzle Sokoban is PSPACE-complete [In: Proc. Internat.  ...  Just as many NP-complete problems become PSPACE-complete when turned into twoplayer games [9] , it is also natural to expect that they become PSPACE-complete when turned into dynamic puzzles.  ... 
doi:10.1016/j.tcs.2005.05.008 fatcat:eyqmplmhanfhxmoiryj4da44ym

The Cyclic-Routing UAV Problem is PSPACE-Complete [article]

Hsi-Ming Ho, Joel Ouaknine
2015 arXiv   pre-print
The special case of there being a single UAV is claimed to be NP-complete in the literature. In this paper, we show that the CR-UAV Problem is in fact PSPACE-complete even in the single-UAV case.  ...  The Cyclic-Routing UAV Problem (CR-UAV) is the question of whether this task has a solution. This problem can straightforwardly be solved in PSPACE by modelling it as a network of timed automata.  ...  The cr-uav Problem is PSPACE-complete. 4 Conclusion We have proved that the cr-uav Problem is PSPACE-complete even in the single-UAV case.  ... 
arXiv:1411.2874v2 fatcat:nyhh32w4l5cqff64yrgim3yauy

The Nondeterministic Constraint Logic Model of Computation: Reductions and Applications [chapter]

Robert A. Hearn, Erik D. Demaine
2002 Lecture Notes in Computer Science  
Finally, we strengthen the existing result that the pushing-blocks puzzle Sokoban is PSPACE-complete [2], by showing that it is PSPACE-complete even if no barriers are allowed. and that sliding-block puzzles  ...  Section 3 proves increasingly simple formulations of NCL to be PSPACE-complete.  ...  problem with a particular box size and set of pieces is in PSPACE.  ... 
doi:10.1007/3-540-45465-9_35 fatcat:kakokh4m6bayzgyvhrsqspcuwu

The Cyclic-Routing UAV Problem is PSPACE-Complete [chapter]

Hsi-Ming Ho, Joël Ouaknine
2015 Lecture Notes in Computer Science  
The special case of there being a single UAV is claimed to be NP-complete in the literature. In this paper, we show that the cr-uav Problem is in fact PSPACE-complete even in the single-UAV case.  ...  The Cyclic-Routing UAV Problem (cr-uav) is the question of whether this task has a solution. This problem can straightforwardly be solved in PSPACE by modelling it as a network of timed automata.  ...  The cr-uav Problem is PSPACE-complete. 4 Conclusion We have proved that the cr-uav Problem is PSPACE-complete even in the single-UAV case.  ... 
doi:10.1007/978-3-662-46678-0_21 fatcat:jkdknoolv5hndbj2gxd3fm2vd4

SOKOBAN and other motion planning problems

Dorit Dor, Uri Zwick
1999 Computational geometry  
Some members of the family are shown to be PSPACE-complete thus improving and extending (and also simplifying) a previous NP-hardness result of Wilfong.  ...  The decision problem corresponding to SOKOBAN is shown to be NP-hard.  ...  SOKOBAN + (k, 1) is PSPACE-complete, for every k 2.  ... 
doi:10.1016/s0925-7721(99)00017-6 fatcat:bqemwwni75hgjctonzjhhvnz2u

Complexity of hierarchically and 1-dimensional periodically specified problems. I: Hardness results [chapter]

Madhav Marathe, Harry Hunt, Richard Stearns, Vankatesh Radhakrishnan
1997 Satisfiability Problem: Theory and Applications  
The black dots represent the variables and the ellipses represent the clauses. The dotted circles denote the crossovers which are replaced by crossover boxes.  ...  . ~ ~~~ ~ 6We say that A C r'* is PSPACE-complete via a size L(n) reduction if A is PSPACE-complete and for any B A* such that B is decidable (non)-deterministically in space S ( n ) = n, B I p A via some  ... 
doi:10.1090/dimacs/035/05 dblp:conf/dimacs/MaratheHSR96 fatcat:2vtydxwygjhwlf4pbphr346k4e

Traversability, Reconfiguration, and Reachability in the Gadget Framework [chapter]

Joshua Ani, Erik D. Demaine, Yevhenii Diomidov, Dylan Hendrickson, Jayson Lynch
2022 Lecture Notes in Computer Science  
We also study the complexity of reconfiguration, where the goal is to bring the system of gadgets to a specified state, proving many cases PSPACE-complete, and showing in some cases that reconfiguration  ...  can be strictly harder than reachability (where the goal is for the agent to reach a specified location), while in other cases, reachability is strictly harder than reconfiguration.  ...  Reconfiguration motion planning is PSPACE-complete for any set of reversible gadgets for which reachability motion planning is PSPACE-complete. Proof.  ... 
doi:10.1007/978-3-030-96731-4_5 fatcat:twq6ly7bhrd2jdrh4q7mq242ie

Page 3443 of Mathematical Reviews Vol. , Issue 84h [page]

1984 Mathematical Reviews  
Chapter 16: Various suboptimal strategies for Dots-and-Boxes and a connection to Kayles and Dawson’s Kayles. Dots-and-Boxes is NP-hard.  ...  For the Exptime-completeness of chess, see an article by the reviewer and D. Lichtenstein [J. Combin. Theory Ser. A 31 (1981), 199-214; MR 83b:68044]. This also implies the Pspace-hardness of chess.  ... 
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