Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Angel_problem> ?p ?o }
Showing triples 1 to 61 of
61
with 100 triples per page.
- Angel_problem abstract "The angel problem is a question in game theory proposed by John Horton Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard (or equivalently the points of a 2D lattice). The angel has a power k (a natural number 1 or higher), specified before the game starts. The board starts empty with the angel at the origin. On each turn, the angel jumps to a different empty square which could be reached by at most k moves of a chess king, i.e. the distance from the starting square is at most k in the infinity norm. The devil, on its turn, may add a block on any single square not containing the angel. The angel may leap over blocked squares, but cannot land on them. The devil wins if the angel is unable to move. The angel wins by surviving indefinitely.The angel problem is: can an angel with high enough power win?There must exist a winning strategy for one of the players. If the devil can force a win then it can do so in a finite number of moves. If the devil cannot force a win then there is always an action that the angel can take to avoid losing and a winning strategy for it is always to pick such a move. More abstractly, the "pay-off set" (i.e., the set of all plays in which the angel wins) is a closed set (in the natural topology on the set of all plays), and it is known that such games are determined.Conway offered a reward for a general solution to this problem ($100 for a winning strategy for an angel of sufficiently high power, and $1000 for a proof that the devil can win irrespective of the angel's power). Progress was made first in higher dimensions. In late 2006, the original problem was solved when independent proofs appeared, showing that an angel can win. Bowditch proved that a 4-angel can win and Máthé and Kloster gave proofs that a 2-angel can win. At this stage, it has not been confirmedby Conway who is to be the recipient of his prize offer, or whether each published and subsequent solution will also earn $100 US.".
- Angel_problem thumbnail Angel_problem.svg?width=300.
- Angel_problem wikiPageExternalLink Angel.pdf.
- Angel_problem wikiPageExternalLink index.html.
- Angel_problem wikiPageExternalLink bhb-angel.pdf.
- Angel_problem wikiPageExternalLink angel-mathe.pdf.
- Angel_problem wikiPageExternalLink angel.pdf.
- Angel_problem wikiPageExternalLink conway.pdf.
- Angel_problem wikiPageID "1076026".
- Angel_problem wikiPageLength "11383".
- Angel_problem wikiPageOutDegree "25".
- Angel_problem wikiPageRevisionID "680112746".
- Angel_problem wikiPageWikiLink Axiom_of_determinacy.
- Angel_problem wikiPageWikiLink Brian_Bowditch.
- Angel_problem wikiPageWikiLink Béla_Bollobás.
- Angel_problem wikiPageWikiLink Category:1996_introductions.
- Angel_problem wikiPageWikiLink Category:Combinatorial_game_theory.
- Angel_problem wikiPageWikiLink Chessboard.
- Angel_problem wikiPageWikiLink Combinatorics,_Probability_and_Computing.
- Angel_problem wikiPageWikiLink Determinacy.
- Angel_problem wikiPageWikiLink Elwyn_Berlekamp.
- Angel_problem wikiPageWikiLink Game_theory.
- Angel_problem wikiPageWikiLink Homicidal_chauffeur_problem.
- Angel_problem wikiPageWikiLink Imre_Leader.
- Angel_problem wikiPageWikiLink Infinity.
- Angel_problem wikiPageWikiLink John_Horton_Conway.
- Angel_problem wikiPageWikiLink Lattice_(group).
- Angel_problem wikiPageWikiLink Martin_Kutz.
- Angel_problem wikiPageWikiLink Natural_number.
- Angel_problem wikiPageWikiLink Player_(game).
- Angel_problem wikiPageWikiLink Péter_Gács.
- Angel_problem wikiPageWikiLink Theoretical_Computer_Science_(journal).
- Angel_problem wikiPageWikiLink Topology.
- Angel_problem wikiPageWikiLink Uniform_norm.
- Angel_problem wikiPageWikiLink Winning_strategy.
- Angel_problem wikiPageWikiLink File:Angel_problem.svg.
- Angel_problem wikiPageWikiLinkText "Angel problem".
- Angel_problem wikiPageWikiLinkText "Angels & Devils".
- Angel_problem wikiPageWikiLinkText "Angels and Devils".
- Angel_problem wikiPageWikiLinkText "angel problem".
- Angel_problem hasPhotoCollection Angel_problem.
- Angel_problem wikiPageUsesTemplate Template:Reflist.
- Angel_problem subject Category:1996_introductions.
- Angel_problem subject Category:Combinatorial_game_theory.
- Angel_problem hypernym Question.
- Angel_problem type Work.
- Angel_problem type Combinatoric.
- Angel_problem comment "The angel problem is a question in game theory proposed by John Horton Conway. The game is commonly referred to as the Angels and Devils game. The game is played by two players called the angel and the devil. It is played on an infinite chessboard (or equivalently the points of a 2D lattice). The angel has a power k (a natural number 1 or higher), specified before the game starts. The board starts empty with the angel at the origin.".
- Angel_problem label "Angel problem".
- Angel_problem sameAs Problema_del_ángel.
- Angel_problem sameAs مسئله_فرشته.
- Angel_problem sameAs Problxc3xa8me_de_lange.
- Angel_problem sameAs Problema_do_anjo.
- Angel_problem sameAs m.043v13.
- Angel_problem sameAs Задача_ангела.
- Angel_problem sameAs Q3140966.
- Angel_problem sameAs Q3140966.
- Angel_problem sameAs 天使问题.
- Angel_problem wasDerivedFrom Angel_problem?oldid=680112746.
- Angel_problem depiction Angel_problem.svg.
- Angel_problem isPrimaryTopicOf Angel_problem.