We study combinatorial games under restricted misère play, where the equality relation is weakened so that games can be equal modulo a subset of games even if they are not in full misère. In a ...dead-ending rule set (e.g., Domineering, Hackenbush), if a player has no move now, then they will never again have a move. Since no nonzero positions are invertible in full misère play, and few are invertible even in restricted play, an important open problem in restricted play is to classify the invertible positions. Modulo dead-ending games, it has been shown that all ends (at least one player cannot move) are invertible, some non-ends are invertible, and that many positions, such as ⁎, are not invertible; however, a complete classification has been an open problem since 2013. We solve this by proving that a game is invertible modulo dead-ending if and only if it is ‘P-free’ — i.e., if neither the game nor any of its followers are previous-win.
N -player partizan games Cincotti, Alessandro
Theoretical computer science,
07/2010, Letnik:
411, Številka:
34
Journal Article
Recenzirano
Odprti dostop
Conway’s theory of partizan games is both a theory of games and a theory of numbers. An extension of this theory to classify partizan games with an arbitrary finite number of players is presented.
The development of intelligence and security structures in Yugoslavia in World War II was done in extremely complex political and security conditions. After the April war and signing the surrender on ...April 17, 1941, the Ministry of Internal Affairs of the Kingdom of Yugoslavia continued to operate within the royal government which was in exile. After the occupation, Yugoslavia was torn apart by the German and Italian forces and their allies and quislings. The territory of the country was torn into two different spheres of interest - German and Italian, as well as four areas of occupation: German, Italian, Hungarian and Bulgarian. This went on until Italy surrendered in 1943. The members of the Croatian Ustaša movement announced the forming of the Independent State of Croatia (NDH), which initially included the territories of Croatia and Bosnia and Herzegovina, and from October 1941, the territory of Srem with the city of Zemun. This paper looks at the work of intelligence and security institutions on the territory of the occupied state at the time, with a special reflection on the development of the safety organs of the partizan movement.
John Horton Conway combined his passion for mathematics with an unquenchable enthusiasm for games. In addition to inventing a bewildering variety of games, he was deeply interested in analyzing them ...to determine how one should play to win.
We find the misère monoids of normal-play canonical-form integer and non-integer numbers. These come as consequences of more general results for the universe of dead-ending games. Left and right ends ...have previously been defined as games in which Left or Right, respectively, have no moves; here we define a dead left (right) end to be a left (right) end whose options are all left (right) ends, and we define a dead-ending game to be one in which all end followers are dead. We find the monoids and partial orders of dead ends, integers, and all numbers, and construct an infinite family of games that are equivalent to zero in the dead-ending universe.
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