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List Of PSPACE-complete Problems
Here are some of the more commonly known problems that are PSPACE-complete when expressed as decision problems. This list is in no way comprehensive. Games and puzzles Generalized game, Generalized versions of: * Amazons (game), Amazons * Atomix (computer game), Atomix * Checkers if a draw is forced after a polynomial number of non-jump moves * Dyson Telescope Game * TipOver, Cross Purposes * Generalized geography, Geography * Two-player game version of Instant Insanity * Ko rule, Ko-free Go (game), Go * Ladder (Go), Ladder capturing in GoGo ladders are PSPACE-complete * m,n,k-game, Gomoku * Hex (board game), Hex * Konane * Lemmings (video game), Lemmings * Node Kayles * Poset Game * Reversi * River Cro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PSPACE-complete
In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (PSPACE, polynomial space) and if every other problem that can be solved in polynomial space can be Polynomial-time reduction, transformed to it in polynomial time. The problems that are PSPACE-complete can be thought of as the hardest problems in PSPACE, the class of decision problems solvable in polynomial space, because a solution to any one such problem could easily be used to solve any other problem in PSPACE. Problems known to be PSPACE-complete include determining properties of regular expressions and context-sensitive grammars, determining the truth of quantified Boolean formula problem, quantified Boolean formulas, step-by-step changes between solutions of combinatorial optimization problems, and many puzzles and games. Theory A problem is defined to be PSPACE-complete if it can be solved using a polynomial amount o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Node Kayles
In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines, or edges meet. * Node (autonomous system), behaviour for an ordinary differential equation near a critical point *Singular point of an algebraic variety, a type of singular point of a curve In science and engineering Spherical geometry * node, the points where a great circle crosses a plane of reference, or the equator of a sphere Astronomy *Orbital node, the points where an orbit crosses a plane of reference ** Lunar node, where the orbits of the Sun and Moon intersect ** Longitude of the ascending node, how orbital nodes are parameterized Biology *Lymph node, an immune system organ used to store white blood cells *Node of Ranvier, periodic gaps in the insulating myelin sheaths of myelinated axons *Sinoatrial node and atrioventricula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toniann Pitassi
Toniann Pitassi is a Canadian-American mathematician and computer scientist specializing in computational complexity theory. She is currently Jeffrey L. and Brenda Bleustein Professor of Engineering at Columbia University and was Bell Research Chair at the University of Toronto. Academic career A native of Pittsburgh, Pitassi earned bachelor's and master's degrees at Pennsylvania State University before moving to the University of Toronto for her doctoral studies; she earned her PhD in 1992 from Toronto under the supervision of Stephen Cook. After postdoctoral studies at the University of California, San Diego and faculty positions at the University of Pittsburgh and University of Arizona, she returned to Toronto in 2001, and was a professor in the University of Toronto Department of Computer Science and University of Toronto Department of Mathematics until 2021, when she joined the faculty of Columbia University. She was an invited speaker at International Congress of Mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pebble Game
In mathematics and computer science, a pebble game is a type of mathematical game played by placing "pebbles" or "markers" on a directed acyclic graph according to certain rules: * A given step of the game consists of either placing a pebble on an empty vertex or removing a pebble from a previously pebbled vertex. * A vertex may be pebbled only if all its predecessors have pebbles. * The objective of the game is to successively pebble each vertex of ''G'' (in any order) while minimizing the number of pebbles that are ever on the graph simultaneously. Running time The trivial solution is to pebble an ''n''-vertex graph in ''n'' steps using ''n'' pebbles. Hopcroft, Paul and Valiant showed that any vertex of an ''n''-vertex graph can be pebbled with O(''n''/log ''n'') pebbles where the constant depends on the maximum in-degree. This enabled them to prove that DTIME(''f''(''n'')) is contained in DSPACE(''f''(''n'')/log ''f''(''n'')) for all time-constructible ''f''. Lipton and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Super Mario Bros
is a 1985 Platformer, platform game developed and published by Nintendo for the Nintendo Entertainment System (NES). It is the successor to the 1983 arcade game ''Mario Bros.'' and the first game in the ''Super Mario'' series. It was originally released in September 1985 in Japan for the Family Computer; following a US test market release for the NES, it was converted to international arcade game, arcades on the Nintendo VS. System in early 1986. The NES version received a wide release in North America that year and in PAL regions in 1987. Players control Mario, or his brother Luigi in the multiplayer mode, to traverse the Mushroom Kingdom in order to rescue Princess Peach, Princess Toadstool from King Koopa (later named Bowser). They traverse side-scrolling video game, side-scrolling stages while avoiding hazards such as enemies and pits with the aid of power-ups such as the Super Mushroom, Fire Flower and Starman (Mario), Starman. The game was designed by Shigeru Miyamot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sokoban
is a puzzle video game in which the player pushes boxes around in a warehouse, trying to get them to storage locations. The game was designed in 1981 by Hiroyuki Imabayashi and first published in Japan in 1982 by his company Thinking Rabbit for the NEC PC-8801 computer. It was later ported to various platforms and followed by new titles. It became popular in Japan and internationally, inspiring unofficial versions, a subgenre of box-pushing puzzle games, and artificial intelligence research. Gameplay The warehouse is a grid composed of floor squares and impassable wall squares. Some floor squares contain a box and some are marked as storage locations. The number of boxes equals the number of storage locations. The player, often represented as a worker character, can move one square at a time horizontally or vertically onto empty floor squares, but cannot pass through walls or boxes. To move a box, the player walks up to it and pushes it to an empty square directly beyond the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scrabble
''Scrabble'' is a word game in which two to four players score points by placing tiles, each bearing a single letter, onto a Board game, game board divided into a 15×15 grid of squares. The tiles must form words that, in crossword fashion, read left to right in rows or downward in columns and are included in a standard dictionary or lexicon. American architect Alfred Mosher Butts invented the game in 1931. ''Scrabble'' is produced in the United States and Canada by Hasbro, under the brands of both of its subsidiaries, Milton Bradley Company, Milton Bradley and Parker Brothers. Mattel owns the rights to manufacture ''Scrabble'' outside the U.S. and Canada. As of 2008, the game is sold in 121 countries and is available in more than 30 languages; approximately 150 million sets have been sold worldwide, and roughly one-third of American homes and half of British homes have a ''Scrabble'' set. There are approximately 4,000 ''Scrabble'' clubs around the world. Equipment ''Scrabble ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Computing
The ''SIAM Journal on Computing'' is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM). Although its official ISO abbreviation is ''SIAM J. Comput.'', its publisher and contributors frequently use the shorter abbreviation ''SICOMP''. SICOMP typically hosts the special issues of the IEEE Annual Symposium on Foundations of Computer Science (FOCS) and the Annual ACM Symposium on Theory of Computing (STOC), where about 15% of papers published in FOCS and STOC each year are invited to these special issues. For example, Volume 48 contains 11 out of 85 papers published in FOCS 2016. References External linksSIAM Journal on Computing on |
Peter Shor
Peter Williston Shor (born August 14, 1959) is an American theoretical computer scientist known for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical computer. He has been a professor of applied mathematics at the Massachusetts Institute of Technology (MIT) since 2003. Early life and education Shor was born on August 14, 1959, in New York City, to Joan Bopp Shor and S. W. Williston Shor.Joan Shor Obituary He grew up in Washington, D.C. and |
Anne Condon
Anne Elizabeth Condon, is an Irish-Canadian computer scientist, professor, and former head of the UBC Computer Science Department, Computer Science Department of the University of British Columbia. Her research focuses on computational complexity theory, DNA computing, and bioinformatics.Faculty web page University of British Columbia, retrieved 2011-11-20.Who We Are: Anne Condon , Anita Borg Institute for Women and Technology, retrieved 2011-11-20. She has also held the Natural Sciences and Engineering Research Council, NSERC/General Motors Canada Chair for Women in Science and Engineering (CWSE) from 2004 to 2009, and has worked to improve the success of women in the sciences and engineeri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mahjong Solitaire
Mahjong solitaire (also known as Shanghai solitaire, electronic or computerized mahjong, solitaire mahjong or simply mahjong) is a single-player matching game that uses a set of mahjong tiles rather than cards. It is more commonly played on a computer than as a tabletop game, although it can be played using physical tiles using a special wooden frame for its lengthy set-up process. Although named after the four-player tile game mahjong, the method of gameplay is unrelated. Play The 144 tiles are arranged in a four-layer pattern with their faces upwards. A tile is said to be open or exposed if it can be moved either left or right without disturbing other tiles. The goal is to match open pairs of identical tiles and remove them from the board, exposing the tiles under them for play. The game is won when all pairs of tiles have been removed from the board, and lost if the remaining tiles contain no exposed pairs. Mathematical analysis Playing Mahjong solitaire optimally in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rush Hour (board Game)
''Rush Hour'' is a sliding block puzzle invented by Nob Yoshigahara in the 1970s. It was first sold in the United States in 1996. It is now being manufactured by ThinkFun (formerly Binary Arts). ThinkFun now sells ''Rush Hour'' spin-offs ''Rush Hour Jr.'', ''Safari Rush Hour'', ''Railroad Rush Hour'', ''Rush Hour Brain Fitness'' and ''Rush Hour Shift'', with puzzles by Scott Kim. The game sold more than 1 million units. Game The board is a 6×6 grid with grooves in the tiles to allow cars to slide, card tray to hold the cards, current active card holder and an exit hole. The game comes with 16 vehicles (12 cars, 4 trucks), each colored differently, and 40 puzzle cards. Cars and trucks are both one square wide, but cars are two squares long and trucks are three squares long. Vehicles can only be moved along a straight line on the grid; rotation is forbidden. Puzzle cards, each with a level number that indicates the difficulty of the challenge, show the starting positions of cars ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
