J. C. Culberson. Sokoban is pspace-complete. In Proceedings of the International Conference on Fun with Algorithms (FUN98), pages 65--76, Waterloo, Ontario, Canada, June 1998. Carleton-Scientific.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....) time to calculate per state, even when reusing information from the parent state. Therefore, much less states can be explored; while for Atomix 1,000,000 states per second can be generated, this number is for Sokoban around 10,000. Sokoban has been shown to be PSPACEcomplete by Culberson [Cul98]. Junghanns has analyzed it thoroughly and written the sophisticated solver program Rolling Stone [Jun99] 4 Complexity of Atomix 4.1 Complexity of Sliding Block Puzzles The time complexity of sliding block puzzles was the subject of intense research in the past. Though seemingly trivial, most ....

Joseph C. Culberson. Sokoban is PSPACE-complete. In Elena Lodi, Linda Pagli, and Nicola Santoro, editors, Proceedings of the International Conference on Fun with Algorithms (FUN98) , pages 65--76. Carleton Scientific, Waterloo, Ontario, June 18--20 1998.

.... Blocks in Gravity is NP hard Erich Friedman Stetson University, DeLand, FL 32720 efriedma stetson.edu Introduction There has been much progress recently showing that certain classes of puzzles involving pushing blocks [2, 3, 4, 10] are NP hard. For example, consider the block pushing puzzle Push k which consists of movable unit square blocks on an integer lattice, and a robot that can move horizontally and vertically to attempt to reach a specified lattice position. The robot can push k blocks provided it pushes them to ....

J. Culberson, "Sokoban is PSPACE complete." Proc. Internet Conf. Fun with Algorithms (1998), N. S. E. Lodi, L. Pagli, Ed., Carelton Scientific, 65-76.

....Since 3 colorability of planar graphs is known to be NP complete [6] this will show that Corral puzzles are NP hard. We complete the proof by showing that a solution to a Corral puzzle can be checked in polynomial time. Similar approaches to proving puzzles are NP complete are taken in [1, 2, 4, 5, 7]. Figure 2. A graph (left) and its corresponding Corral blueprint (right) Wires Our wires will be rectangles of width 3 in the Corral puzzle, with every fourth row containing 2 in the left column and 12 in the middle column. A wire can be locally solved in essentially 3 different ways, as shown ....

J. Culberson, "Sokoban is PSPACE complete." Proc. Internet Conf. Fun with Algorithms (1998), N. S. E. Lodi, L. Pagli, Ed., Carelton Scientific, 65-76.

....values, and junctions in these wires simulate logical gates. The question of whether a solution exists corresponds to the canonical NP complete problem Satisfiability [3] which asks whether a set of truth values for the inputs exists that makes the output true. Similar approaches are taken in [1, 2, 4 8]. The Construction We will refer to a block with label n as an n block. Our wires will be passageways for blocks to move in. A wire carries the value TRUE is there is a 1 block moving through it, and the value FALSE otherwise. To create our inputs and outputs, we need to have variables which ....

J. Culberson, "Sokoban is PSPACE-complete." preprint.

....form the given molecule Obviously, this problem can be formalized as a state space search problem, which recently was undertaken by H u ner et al. 9] There di erent heuristic search methods were presented. Atomix falls into the category of sliding block puzzles as, e.g. PushPush [3] Sokoban [2, 4], or 15Puzzle [12] where time and space complexity was, and still is, subject of intense research. Though seemingly trivial, most variations are at least NP hard, and contained in PSPACE; some are even PSPACE complete we refer the reader to, e.g. Balc azar et al. 1] for further details on ....

....Is it 2D or 3D 1. 2. 3. 4. 5. 6. 7. 8. 9. Game Robot Pull Blocks Fixed # Path Slide Dim. Complexity PushPush3D unit 1 3D NP hard [11] PushPush unit 1 2D NP hard [3] Push unit k 2D NP hard [7] Sokoban 1 2 2 2D PSPACE compl. 4] Sokoban unit 1 2D PSPACE compl. [2] 15 Puzzle unit 1 2D NP hard [12] RushHour 1 f2; 3g 1 2D PSPACE compl. 5] Atomix unit 1 2D PSPACE compl. Bricks variable 1 2D PSPACE compl. 8] 1. 2. 3. 4. 5. 6. 7. 8. 9. Game Robot Pull Blocks Fixed # Path Slide Dim. Complexity PushPush3D unit 1 3D NP hard [11] PushPush ....

[Article contains additional citation context not shown here]

J. Culberson. Sokoban is PSPACE-complete. In International Conference on Fun with Algorithms, Proceedings in Informatics 4, pages 65-76, Elba, Italy, June 1999. Carleton Scientic, Waterloo, Canada.

....of the puzzle: is it 2D or 3D 1. 2. 3. 4. 5. 6. 7. 8. 9. Game Robot Pull Blocks Fixed # Path Slide Dim. Complexity PushPush3D unit 1 3D NP hard PushPush unit 1 2D NP hard Push unit k 2D NP hard Sokoban 1 2 2 2D PSPACE compl. Sokoban unit 1 2D PSPACE compl. [1] 15 Puzzle unit 1 2D NP compl. 17] Rush Hour 1 2,3 1 2D PSPACE compl. Atomix unit 1 2D PSPACE compl. 12] 4.2 A Formal De nition of Atomix We will now give a formal de nition of an Atomix problem instance (level ) De nition 1. An Atomix problem instance consists of: A nite set ....

J. C. Culberson. Sokoban is PSPACE-complete. In E. Lodi, L. Pagli, and N. Santoro, editors, Proc. FUN-98, pp. 6576. Carleton Scientic, Waterloo, 1998.

....1#2 # 6 3 # 6 # # 1#2 # 6#3 # 6 # # .For small values of # experimental data as given in [11] matches this analytical study. The observed asymptotic branching factor is 6 3 # 6=13#34846923 as expected. Extending the work to problem domains like the PSPACE complete Sokoban problem [1] is challenging. It is dicult to derive an accurate prediction, since the branching behavior of the tree includes almost all state facets. Therefore, a more complicated search model has to be devised to derive exact or approximate search tree prediction in this domain. As Andreas Junghanns has ....

J. C. Culberson. Sokoban is PSPACE-complete. In ### ### ########## #####, pages 65-76. Carleton Scientic, 1998.

....2D or 3D 1. 2. 3. 4. 5. 6. 7. 8. 9. Game Robot Pull Blocks Fixed # Path Slide Dim. Complexity PushPush3D # # unit # # # # 3D NP hard PushPush # # unit # # # # 2D NP hard Push # # # unit # # # # 2D NP hard Sokoban # # 1#2 # # # # 2D PSPACE compl. Sokoban # # unit # # # # 2D PSPACE compl. [1] 15 Puzzle # unit # # # # 2D NP compl. 17] Rush Hour # 1# 2,3 # # # # 2D PSPACE compl. Atomix # unit # # # # 2D PSPACE compl. 12] 4.2 AFormal De nition of Atomix We will now give a formal de nition of an Atomix problem instance (level ) De nition 1. AnAtomix problem instanceconsists of: ....

J. C. Culberson. Sokoban is PSPACE-complete. In E. Lodi, L. Pagli, and N. Santoro, editors, ##### ######, pp. 6576. Carleton Scientic, Waterloo, 1998.

....As robots become more powerful at manipulation, an understanding of such models becomes increasingly important. Currentday applications include automated warehouse control and warehouse navigation; see, e.g. 9] A representative abstraction of such applications is the popular Sokoban puzzle [3, 8], which is known to be PSPACEcomplete [3] In this paper we study several variations of simpler puzzles, and show all of these models are NP hard using a reductions from 3 coloring of planar graphs [10] Some variations are additionally known to be NP complete, others PSPACE complete, while the ....

....an understanding of such models becomes increasingly important. Currentday applications include automated warehouse control and warehouse navigation; see, e.g. 9] A representative abstraction of such applications is the popular Sokoban puzzle [3, 8] which is known to be PSPACEcomplete [3]. In this paper we study several variations of simpler puzzles, and show all of these models are NP hard using a reductions from 3 coloring of planar graphs [10] Some variations are additionally known to be NP complete, others PSPACE complete, while the complexity of most variations is unresolved ....

Culberson, J. Sokoban is PSPACE-complete. In Proc. Internat. Conf. Fun with Algorithms (Elba, Italy, June 1998), N. S. E. Lodi, L. Pagli, Ed., Carelton Scienti c, pp. 65-76.

....As robots become more powerful at manipulation, an understanding of such models becomes increasingly important. Current day applications include automated warehouse control and warehouse navigation; see, e.g. 8] A representative abstraction of such applications is the popular Sokoban puzzle [2, 7], which is known to be PSPACE complete [2] In this paper we study several variations of simpler puzzles, and show all of these models are NP hard using a reductions from 3 coloring of planar graphs [9] Some variations are additionally known to be NP complete, others PSPACE complete, while the ....

....an understanding of such models becomes increasingly important. Current day applications include automated warehouse control and warehouse navigation; see, e.g. 8] A representative abstraction of such applications is the popular Sokoban puzzle [2, 7] which is known to be PSPACE complete [2]. In this paper we study several variations of simpler puzzles, and show all of these models are NP hard using a reductions from 3 coloring of planar graphs [9] Some variations are additionally known to be NP complete, others PSPACE complete, while the complexity of most variations is unresolved ....

Culberson, J. Sokoban is PSPACE-complete. In Proc. Internat. Conf. Fun with Algorithms (Elba, Italy, June 1998), Carleton Scientic, pp. 65-76.

.... Observe that the way we define continuity leaves room for the necessary indeterminism: Usually one would require that the output elements are given by continuous functions in the input, but here both the path of the input and the path of the output are given by continuous functions on the interval [0,1]. The following property of continuous evaluations is crucial: Lemma 2.11. If there exists a continuous evaluation of the GSP P over the JMB for a continuous movement p i t then it is unique. PROOF. We can prove this lemma by induction on the length of P. Assuming that the statement holds for ....

J. CULBERSON, Sokoban is PSPACE-complete, Proceedings in Informatics 4, Fun With Algorithms, E. Lodi, L. Pagli and N. Santoro Eds. pp 65-76, Carleton Scientific, Waterloo. 1999.

....planning problem [ Dor and Zwick, 1995 ] Sokoban is analogous to the problem of having a robot in a warehouse move specified goods from their current location to their final destination, subject to the topology of the warehouse and any obstacles in the way. Sokoban has been shown to be NP hard [ Culberson, 1997; Dor and Zwick, 1995 ] Previously we reported on our attempts to solve Sokoban problems using the standard single agent search techniques available in the literature [ Junghanns and Schaeffer, 1998c ] When these proved inadequate, solving only 10 of a 90 problem test suite, new algorithms ....

J. Culberson. Sokoban is PSPACEcomplete. Technical Report TR97--02, Dept. of Computing Science, University of Alberta, 1997. ftp.cs.ualberta.ca/pub/TechReports/1997/TR97--02.

....[BOS94] More firm are the results on Sokoban, a computer game that restricts the pushing robot to only push one block at a time, and requires the storing of (some or all) blocks into designated storage locations. This game was proved NP hard in [DZ95] and PSPACE complete by Culberson [Cul98]. Here we emphasize another theme: finding a nontrivial version of the game that is not intractable. To date only the most uninteresting versions are known to be solvable in polynomial time, for example, where the robot s path must be monotonic [DO92] To explore the variety of pushing block ....

.... pushed, or do they slide the maximal amount of their free range If our goal is to find the weakest robot and most unconstrained puzzle conditions that still lead to intractability, it is reasonable to consider robots who can only push (1) and to restrict all blocks to be unit squares (2) as in [DO92, DZ95, Cul98], for permitting robots to pull, and permitting blocks of other shapes, makes it relatively easy to construct intractable puzzles. It also makes sense to explore the goal of simply finding a path (5) as in [Wil91, DO92] rather than the more challenging task of storing the blocks as in Sokoban ....

[Article contains additional citation context not shown here]

J. Culberson. Sokoban is PSPACE-complete. In Proc. Internat. Conf. Fun with Algorithms, pages 65--76, Elba, Italy, June 1998. Carleton Scientific.

....[BOS94] More firm are the results on Sokoban, a computer game that restricts the pushing robot to only push one block at a time, and requires the storing of (some or all) blocks into designated storage locations. This game was proved NP hard in [DZ95] and PSPACE complete by Culberson [Cul98]. Here we emphasize another theme: finding a nontrivial version of the game that is not intractable. To date only the most uninteresting versions are known to be solvable in polynomial time, for example, where the robot s path must be monotonic [DO92] To explore the variety of pushing block ....

.... pushed, or do they slide the maximal amount of their free range If our goal is to find the weakest robot and most unconstrained puzzle conditions that still lead to intractability, it is reasonable to consider robots who can only push (1) and to restrict all blocks to be unit squares (2) as in [DO92, DZ95, Cul98], for permitting robots to pull, and permitting blocks of other shapes, makes it relatively easy to construct intractable puzzles. It also makes sense to explore the goal of simply finding a path (5) as in [Wil91, DO92] rather than the more challenging task of storing the blocks as in Sokoban ....

[Article contains additional citation context not shown here]

J. Culberson. Sokoban is PSPACE-complete. In Proc. Internat. Conf. Fun with Algorithms, pages 65--76, Elba, Italy, June 1998. Carleton Scientific.

....mldemaineg uwaterloo.ca. y Dept. Comput. Sci. Smith College, Northampton, MA 01063, USA. orourke cs.smith.edu. Supported by NSF grant CCR 9731804. 1 storing of (some or all) blocks into designated storage locations. This game was proved NP hard in [DZ95] and PSPACE complete by Culberson [Cul98]. Here we emphasize another theme: finding a nontrivial version of the game that is not intractable. To date only the most uninteresting versions are known to be solvable in polynomial time, for example, where the robot s path must be monotonic [DO92] We explore a different version, again ....

....of their free range 7. The dimension of the puzzle: 2D or 3D If our goal is to find the weakest robot and most unconstrained puzzle conditions that still lead to intractability, it is reasonable to consider robots who can only push (1) and to restrict all blocks to be unit squares (2) as in [DO92, DZ95, Cul98], for permitting robots to pull, and permitting blocks of other shapes, makes it relatively easy to construct intractable puzzles. It also makes sense to explore the goal of simply finding a path (5) as in [Wil91, DO92] rather than the more challenging task of storing the blocks as in Sokoban ....

[Article contains additional citation context not shown here]

J. Culberson. Sokoban is PSPACE-complete. In Proc. Internat. Conf. Fun with Algorithms, pages 65--76, Elba, Italy, June 1998. Carleton Scientific.

....Judy Franklin, Biliana Kaneva, Haley Miller, Anton Okmianski, Irena Pashchenko, Ileana Streinu, Geetika Tewari, Dominique Thi ebaut, Elif Tosun. i storing of (some or all) blocks into designated storage locations. This game was proved NP hard in [DZ95] and PSPACE complete by Culberson [Cul98]. Here we emphasize another theme: finding a nontrivial version of the game that is not intractable. To date only the most uninteresting versions are known to be solvable in polynomial time, for example, where the robot s path must be monotonic [DO92] We explore a different version, again ....

....of their free range 7. The dimension of the puzzle: 2D or 3D If our goal is to find the weakest robot and most unconstrained puzzle conditions that still lead to intractability, it is reasonable consider robots who can only push (1) and to restrict all blocks to be unit squares (2) as in [DO92, DZ95, Cul98], for permitting robots to pull, and permitting blocks of other shapes, makes it relatively easy to construct intractable puzzles. It also makes sense to explore the goal of simply finding a path (5) as in [Wil91, DO92] rather than the more challenging task of storing the blocks as in Sokoban ....

[Article contains additional citation context not shown here]

J. Culberson. Sokoban is PSPACE-complete. In Proc. Internat. Conf. Fun with Algorithms, pages 65--76, Elba, Italy, June 1998. Carelton Scientific.

....file is maintained showing who has solved which prob lems and how efficient their solution is (also at http: xsokoban.lcs.mit.edu xsokoban.html) Thus solving a problem is only part of the satisfaction; improving on your solution is equally important. Sokoban has been shown to be NP hard [ Culberson, 1997; Dor and Zwick, 1995 ] Dor and Zwick, 1995 ] show that the game is an instance of a motion planning problem, and compare the game to other motion planning problems in the literature. For example, Sokoban is similar to Wilfong s work with movable obstacles, where the man is allowed to hold on ....

Joe Culberson. Sokoban is pspacecomplete. Technical Report TR 97-02, Dept. of Computing Science, University of Alberta, 1997. also: http://web.cs.ualberta.ca/~joe/Preprints/Sokoban.

....planning problem [ Dor and Zwick, 1995 ] Sokoban is analogous to the problem of having a robot in a warehouse move specified goods from their current location to their final destination, subject to the topology of the warehouse and any obstacles in the way. Sokoban has been shown to be NP hard [ Culberson, 1997; Dor and Zwick, 1995 ] Previously we reported on our attempts to solve Sokoban problems using the standard single agent search techniques available in the literature [ Junghanns and Schaeffer, 1998c ] When these proved inadequate, solving only 10 of a 90 problem test suite, new algorithms had ....

J. Culberson. Sokoban is PSPACEcomplete. Technical Report TR97--02, Dept. of Computing Science, University of Alberta, 1997. ftp.cs.ualberta.ca/pub/TechReports/1997/TR97--02.

....the solution length by at most one, but may increase it by an arbitrary amount. Optimizing the man movements involves using non unitary changes to the lower bound (the number of man movements it takes to position the man behind a stone to do the push) Sokoban has been shown to be NP hard [Cul97,DZ95]. DZ95] show that the game is an instance of a motion planning problem, and compare the game to other motion planning problems in the literature. For example, Sokoban is similar to Wilfong s work with movable obstacles, where the man is allowed to hold on to the obstacle and move with it, as if ....

J. Culberson. Sokoban is PSPACE-complete. Technical Report TR 97-02, Dept. of Computing Science, University of Alberta, 1997. Also: http://web.cs.ualberta.ca/~joe/Preprints/Sokoban.

No context found.

J. C. Culberson. Sokoban is pspace-complete. In Proceedings of the International Conference on Fun with Algorithms (FUN98), pages 65--76, Waterloo, Ontario, Canada, June 1998. Carleton-Scientific.

No context found.

J. Culberson, Sokoban is PSPACE-complete, Proceedings in Informatics 4, Fun With Algorithms, E. Lodi, L. Pagli and N. Santoro Eds. pp 65-76, Carleton Scientific, Waterloo. 1999.

No context found.

J. Culberson. Sokoban is PSPACE-complete. In Proc. Internat. Conf. Fun with Algorithms, pp. 65-76, Elba, Italy, June 1998.

No context found.

J. Culberson, "Sokoban is PSPACE-complete." Proc. Internet Conf. Fun with Algorithms (1998), N. S. E. Lodi, L. Pagli, Ed., Carelton Scientific, 65-76.

No context found.

J. Culberson, "Sokoban is PSPACE complete." Proc. Internet Conf. Fun with Algorithms (1998), N. S. E. Lodi, L. Pagli, Ed., Carelton Scientific, 65-76.

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